arXiv subjects

Ketan Savla

Publications and source records attributed to Ketan Savla.

At least 19 recordsLinked to original sources

arXiv2026

FNO$^{\angle θ}$: Extended Fourier neural operator for learning state and optimal control of distributed parameter systems

We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle, we show that any state and optimal control of linear PDEs with constant coefficients can be represented as an integral in the complex domain. The integrand of this representation involves the same exponential term as in the inverse Fourier transform, where the latter is used to represent the convolution operator in FNO layer. Motivated by this observation, we modify the FNO layer by extending the frequency variable in the inverse Fourier transform from the real to complex domain to capture the integral representation from the fundamental principle. We illustrate the performance of FNO in learning state and optimal control for the nonlinear Burgers' equation, showing order of magnitude improvements in training errors and more accurate predictions of non-periodic boundary values over FNO.

cs.LG↗

arXiv2026

On Online Control of Opinion Dynamics

Networked multi-agent dynamical systems have been used to model how individual opinions evolve over time due to the opinions of other agents in the network. Particularly, such a model has been used to study how a planning agent can be used to steer opinions in a desired direction through repeated, budgeted interventions. In this paper, we consider the problem where individuals' susceptibilities to external influences are unknown. We propose an online algorithm that alternates between estimating this susceptibility parameter, and using the current estimate to drive the opinion to a desired target. We provide conditions that guarantee stability and convergence to the desired target opinion when the planning agent faces budgetary or temporal constraints. Our analysis shows that the key advantage of estimating the susceptibility parameter is that it helps achieve near-optimal convergence to the target opinion given a finite amount of intervention rounds, and, for a given intervention budget, quantifies how close the opinion can get to the desired target.

cs.SI↗

arXiv2025

Constrained bilinear optimal control of reactive evolution equations

We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are imposed on the state and control variables. These PDEs represent a wide range of physical phenomena in fluid flow, heat, and mass transfer. Existing computational methods for this type of control problems only consider constraints on the control variable and lack global convergence guarantee. In this paper, we propose a novel optimize-then-discretize framework for computing constrained bilinear optimal control with both state and control constraints. Unlike existing methods that derive optimality conditions directly from the PDE constraint, this framework first replaces the PDE constraint with an equivalent integral representation of the PDE solution and then derives optimality conditions for the reformulated problem. The integral representation, derived from the unified transform method, does not involve differential operators, and thus explicit expressions for necessary conditions of optimality can be derived using the Karush-Kuhn-Tucker conditions for infinite-dimensional optimization. Discretizing the optimality conditions results in a system of finite-dimensional smooth nonlinear equations, which can be efficiently solved using existing algorithms with guaranteed global convergence at a quadratic rate. This is in contrast with discretize-then-optimize methods that discretize the PDE first and then solve the optimality conditions of the approximated finite-dimensional problem. Computational results for two applications, namely nuclear reactivity control and water quality treatment in a reactor, are presented to illustrate the effectiveness of the proposed framework.

physics.comp-ph↗

arXiv2025

A complex spatial frequency approach to optimal control of finite-extent linear evolution systems

We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for closed-form optimal control only apply to homogeneous (zero) boundary conditions, often resulting in series representations. In this paper, we consider general smooth boundary conditions. We use the unified transform, namely the Fourier transform restricted to the bounded spatial domain, to decouple PDEs into a family of ordinary differential equations (ODEs) parameterized by complex spatial frequency variables. Then, optimal control in the frequency domain is derived using LQR theory for ODEs. The inverse Fourier transform leads to non-causal terms in optimal control corresponding to integrals, over the real line, of future values of unspecified boundary conditions. To eliminate this non-causality, we deform the integrals to well-constructed contours in the complex plane along which the contribution of unknowns vanishes. For the reaction-diffusion equation, we show that the integral representation can be reformulated as a series representation, which leads to a state-feedback convolution form for optimal control, with the boundary conditions appearing as an additive term. In numerical experiments, we illustrate the computational advantages of the integral representation in comparison to the series representation and structural properties of the convolution kernel.

eess.SY↗

arXiv2025

Throughput Maximizing Takeoff Scheduling for eVTOL Vehicles in On-Demand Urban Air Mobility Systems

Urban Air Mobility (UAM) offers a solution to current traffic congestion by using electric Vertical Takeoff and Landing (eVTOL) vehicles to provide on-demand air mobility in urban areas. Effective traffic management is crucial for efficient operation of UAM systems, especially for high-demand scenarios. In this paper, we present a centralized framework for conflict-free takeoff scheduling of eVTOLs in on-demand UAM systems. Specifically, we provide a scheduling policy, called VertiSync, which jointly schedules UAM vehicles for servicing trip requests and rebalancing, subject to safety margins and energy requirements. We characterize the system-level throughput of VertiSync, which determines the demand threshold at which the average waiting time transitions from being stable to being increasing over time. We show that the proposed policy maximizes throughput for sufficiently large fleet size and if the UAM network has a certain symmetry property. We demonstrate the performance of VertiSync through a case study for the city of Los Angeles, and show that it significantly reduces average passenger waiting time compared to a first-come first-serve scheduling policy.

eess.SY↗

arXiv2025

Output-feedback adaptive model predictive control for ramp metering: a set-membership approach

Ramp metering, which regulates the flow entering the freeway, is one of the most effective freeway traffic control methods. This paper introduces an output-feedback adaptive approach to ramp metering that combines model predictive control (MPC) with set-membership parameter and state estimation. The set-membership estimator is based on a mixed-monotone embedding of underlying traffic dynamics. The embedding is also used as the modeling basis for MPC optimization. For a freeway stretch with unknown parameters and partial measurement on the freeway mainline, we provide sufficient conditions on the control horizon, cost functions, terminal sets of MPC, and inflow demand at the ramps such that the queue lengths in the closed-loop system remain bounded. The sufficient condition on the demand matches the necessary condition, thereby proving maximal throughput under the proposed controller. The result is strengthened to input-to-state stability when model parameters and demand are known. The stability analysis is conducted for the case of constant demand and unbounded on-ramps. The closed-loop trajectory data generated by the proposed controller is shown to facilitate finite time estimation of free-flow model parameters, i.e., free-flow speed and turning ratios. Simulation results illustrate stability of the closed-loop system under the proposed controller with time-varying demand and few mainline measurements, for which the system becomes unstable under a well-known approach from the literature. This indicates that the proposed controller renders higher throughput than the well-known approach, possibly using more computing resources.

eess.SY↗

arXiv2025

Adaptive model predictive control for traffic signal timing with unknown demand and parameters

This paper designs traffic signal control policies for a network of signalized intersections without knowing the demand and parameters. Within a model predictive control (MPC) framework, control policies consist of an algorithm that estimates parameters and a one-step MPC that computes control inputs using estimated parameters. The algorithm switches between different terminal sets of the MPC to explore different regions of the state space, where different parameters are identifiable. The one-step MPC minimizes a cost that approximates the sum of squares of all the queue lengths within a constant and does not require demand information. We show that the algorithm can estimate parameters exactly in finite time, and the one-step MPC renders maximum throughput in terms of input-to-state practical stability. Simulations indicate better transient performance regarding queue lengths under our proposed policies than existing ones.

eess.SY↗

arXiv2024

A Traffic Management Framework for On-Demand Urban Air Mobility Systems

Urban Air Mobility (UAM) offers a solution to current traffic congestion by providing on-demand air mobility in urban areas. Effective traffic management is crucial for efficient operation of UAM systems, especially for high-demand scenarios. In this paper, we present a centralized traffic management framework for on-demand UAM systems. Specifically, we provide a scheduling policy, called VertiSync, which schedules the aircraft for either servicing trip requests or rebalancing in the system subject to aircraft safety margins and energy requirements. We characterize the system-level throughput of VertiSync, which determines the demand threshold at which passenger waiting times transition from being stabilized to being increasing over time. We show that the proposed policy is able to maximize throughput for sufficiently large fleet sizes. We demonstrate the performance of VertiSync through a case study for the city of Los Angeles, and show that it significantly reduces passenger waiting times compared to a first-come first-serve scheduling policy.

cs.NI↗

arXiv2023

Ramp Metering to Maximize Freeway Throughput under Vehicle Safety Constraints

We consider Ramp Metering (RM) at the microscopic level subject to vehicle following safety constraints for a freeway with arbitrary number of on- and off-ramps. The arrival times of vehicles to the on-ramps, as well as their destinations are modeled by exogenous stochastic processes. Once a vehicle is released from an on-ramp, it accelerates towards the free flow speed if it is not obstructed by another vehicle; once it gets close to another vehicle, it adopts a safe gap vehicle following behavior. The vehicle exits the freeway once it reaches its destination off-ramp. We design traffic-responsive RM policies that maximize the throughput. For a given routing matrix, the throughput of a RM policy is characterized by the set of on-ramp arrival rates for which the expected queue size at all the on-ramps remain bounded. The proposed RM policies work in synchronous cycles during which an on-ramp does not release more vehicles than its queue size at the beginning of the cycle. Moreover, all the policies operate under vehicle following safety constraints, where new vehicles are released only if there is sufficient gap between vehicles on the mainline at the moment of release. We provide three mechanisms under which each on-ramp: (i) pauses release for a time interval at the end of a cycle, or (ii) adjusts the release rate during a cycle, or (iii) adopts a conservative safe gap criterion for release during a cycle. All the proposed policies are reactive, meaning that they only require real-time traffic measurements without the need for demand prediction. The throughput of these policies is characterized by studying stochastic stability of the induced Markov chains, and is proven to be maximized when the merging speed at all the on-ramps equals the free flow speed. Simulations are provided to illustrate the performance of our policies and compare with a well-known RM policy from the literature.

math.PR↗

arXiv2023

Throughput of Freeway Networks under Ramp Metering Subject to Vehicle Safety Constraints

Ramp metering is one of the most effective tools to combat traffic congestion. In this paper, we present a ramp metering policy for a network of freeways with arbitrary number of on- and off-ramps, merge, and diverge junctions. The proposed policy is designed at the microscopic level and takes into account vehicle following safety constraints. In addition, each on-ramp operates in cycles during which it releases vehicles as long as the number of releases does not exceed its queue size at the start of the cycle. Moreover, each on-ramp dynamically adjusts its release rate based on the traffic condition. To evaluate the performance of the policy, we analyze its throughput, which is characterized by the set of arrival rates for which the queue sizes at all on-ramps remain bounded in expectation. We show that the proposed policy is able to maximize the throughput if the merging speed at all the on-ramps is equal to the free flow speed and the network has no merge junction. We provide simulations to illustrate the performance of our policy and compare it with a well-known policy from the literature.

eess.SY↗

arXiv2022

An Experimental Study on Learning Correlated Equilibrium in Routing Games

We study route choice in a repeated routing game where an uncertain state of nature determines link latency functions, and agents receive private route recommendation. The state is sampled in an i.i.d. manner in every round from a publicly known distribution, and the recommendations are generated by a randomization policy whose mapping from the state is known publicly. In a one-shot setting, the agents are said to obey recommendation if it gives the smallest travel time in a posteriori expectation. A plausible extension to repeated setting is that the likelihood of following recommendation in a round is related to regret from previous rounds. If the regret is of satisficing type with respect to a default choice and is averaged over past rounds and over all agents, then the asymptotic outcome under an obedient recommendation policy coincides with the one-shot outcome. We report findings from an experiment with one participant at a time engaged in repeated route choice decision on computer. In every round, the participant is shown travel time distribution for each route, a route recommendation generated by an obedient policy, and a rating suggestive of average experience of previous participants with the quality of recommendation. Upon entering route choice, the actual travel times are revealed. The participant evaluates the quality of recommendation by submitting a review. This is combined with historical reviews to update rating for the next round. Data analysis from 33 participants each with 100 rounds suggests moderate negative correlation between the display rating and the average regret, and a strong positive correlation between the rating and the likelihood of following recommendation. Overall, under obedient recommendation policy, the rating converges close to its maximum value by the end of the experiments in conjunction with very high frequency of following recommendations.

cs.GT↗

arXiv2022

Convergence in a Repeated Non-atomic Routing Game with Partial Signaling

We study the following repeated non-atomic routing game. In every round, nature chooses a state in an i.i.d. manner according to a publicly known distribution, which influences link latency functions. The system planner makes private route recommendations to participating agents, which constitute a fixed fraction, according to a publicly known signaling strategy. The participating agents choose between obeying or not obeying the recommendation according to cumulative regret of the participating agent population in the previous round. The non-participating agents choose route according to myopic best response to a calibrated forecast of the routing decisions of the participating agents. We show that, for parallel networks, if the planner's signal strategy satisfies the obedience condition, then, almost surely, the link flows are asymptotically consistent with the Bayes correlated equilibrium induced by the signaling strategy.

eess.SY↗

arXiv2021

Information Design for a Non-atomic Service Scheduling Game

We study an information design problem for a non-atomic service scheduling game. The service starts at a random time and there is a continuum of agent population who have a prior belief about the service start time but do not observe the actual realization of it. The agents want to make decisions of when to join the queue in order to avoid long waits in the queue or not to arrive earlier than the service has started. There is a planner who knows when the service starts and makes suggestions to the agents about when to join the queue through an obedient direct signaling strategy, in order to minimize the average social cost. We characterize the full information and the no information equilibria and we show in what conditions it is optimal for the planner to reveal the full information to the agents. Further, by imposing appropriate assumptions on the model, we formulate the information design problem as a generalized problem of moments (GPM) and use computational tools developed for such problems to solve the problem numerically.

eess.SY↗

arXiv2021

Information Design in Non-atomic Routing Games with Partial Participation: Computation and Properties

We consider a routing game among non-atomic agents where link latency functions are conditional on an uncertain state of the network. The agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signaling policy respectively. The remaining agents choose route according to Bayes Nash flow with respect to the prior. We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency over all public or obedient private signaling policies. For a fixed flow induced by non-participating agents, design of an optimal private signaling policy is shown to be a generalized problem of moments for polynomial link latency functions, and to admit an atomic solution with a provable upper bound on the number of atoms. This implies that, for polynomial link latency functions, information design can be equivalently cast as a polynomial optimization problem. This in turn can be arbitrarily lower bounded by a known hierarchy of semidefinite relaxations. The first level of this hierarchy is shown to be exact for the basic two link case with affine latency functions. We also identify a class of private signaling policies over which the optimal social cost is non-increasing with increasing fraction of participating agents for parallel networks. This is in contrast to existing results where the cost of participating agents under a fixed signaling policy may increase with their increasing fraction.

cs.GT↗

arXiv2021

Vehicle Following On A Ring Road Under Safety Constraints: Role of Connectivity and Coordination

A fundamental problem in traffic networks is driving under safety and limited physical space constraints. In this paper, we design longitudinal vehicle controllers and study the dynamics of a system of homogeneous vehicles on a single-lane ring road in order to understand the interplay of limited space, speed, and safety. Each vehicle in the system either operates in the cruise control mode or follows a vehicle ahead by keeping a safe time headway. We show that if the number of vehicles is less than a certain critical threshold, vehicles can occupy the limited space in many different configurations, i.e., different platoons of different sizes, and they converge to a uniform maximum speed while attenuating errors in the relative spacing upstream a platoon. If the number of vehicles exceeds the threshold, vehicles converge to a unique symmetric configuration and the equilibrium speed decreases as the number of vehicles increases. Next, we consider vehicle-to-vehicle (V2V) communication and show that it increases the critical number of vehicles that can travel with the maximum speed. Finally, we consider central coordination and show that the proposed controllers can force vehicles to converge to a desired configuration specified by the coordinator while maintaining safety and comfort. We demonstrate the performance of the proposed controllers via simulation.

eess.SY↗

arXiv2019

Network Effects on Robustness of Dynamic Systems

We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss the effect of physical constraints on robustness to loss in link capacities. In the dynamical setting, we review several settings in which small gain type analysis provides tight robustness guarantees for linear dynamics over finite networks towards worst-case and stochastic disturbances. We also discuss network flow dynamic settings where nonlinear techniques facilitate in understanding the effect on robustness of constraints on capacity and information, substituting information with control action, and cascading failure. We also contrast the latter with a representative contagion model. For asymptotically large networks, we discuss the role of network properties in connecting microscopic shocks to emergent macroscopic fluctuations under linear dynamics as well as for economic networks at equilibrium. Through the review of these results, the paper aims to achieve two objectives. First, to highlight selected settings in which the role of interconnectivity structure of a network on its robustness is well-understood. Second, to highlight a few additional settings in which existing system theoretic tools give tight robustness guarantees, and which are also appropriate avenues for future network-theoretic investigations.

eess.SY↗

arXiv2018

A Decentralized Optimal Feedback Flow Control Approach for Transport Networks

Finite-time optimal feedback control for flow networks under information constraints is studied. By utilizing the framework of multi-parametric linear programming, it is demonstrated that when cost/constraints can be modeled or approximated by piecewise-affine functions, the optimal control has a closed-form state-feedback realization. The optimal feedback control law, however, has a centralized structure and requires instantaneous access to the state of the entire network that may lead to prohibitive communication requirements in large-scale complex networks. We subsequently examine the design of a decentralized optimal feedback controller with a one-hop information structure, wherein the optimum outflow rate from each segment of the network depends only on the state of that segment and the state of the segments immediately downstream. The decentralization is based on the relaxation of constraints that depend on state variables that are unavailable according to the information structure. The resulting decentralized control scheme has a simple closed-form representation and is scalable to arbitrary large networks; moreover, we demonstrate that, with respect to certain meaningful performance indexes, the performance loss due to decentralization is zero; namely, the centralized optimal controller has a decentralized realization with a one-hop information structure and is obtained at no computational/communication cost.

eess.SY↗

arXiv2017

Computing Optimal Control of Cascading Failure in DC Networks

We consider discrete-time dynamics, for cascading failure in DC networks, whose map is composition of failure rule with control actions. Supply-demand at the nodes is monotonically non-increasing under admissible control. Under the failure rule, a link is removed permanently if its flow exceeds capacity constraints. We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply-demand at the nodes, to a feasible state, i.e., a state which is invariant under the failure rule. There is no running cost and the reward associated with a feasible terminal state is the associated cumulative supply-demand. We propose two approaches for computing optimal control. The first approach, geared towards tree reducible networks, decomposes the global problem into a system of coupled local problems, which can be solved to optimality in two iterations. When restricted to the class of one-shot control actions, the optimal solutions to the local problems possess a piecewise affine property, which facilitates analytical solution. The second approach computes optimal control by searching over the reachable set, which is shown to admit an equivalent finite representation by aggregation of control actions leading to the same reachable active link set. An algorithmic procedure to construct this representation is provided by leveraging and extending tools for arrangement of hyperplanes and polytopes. Illustrative simulations, including showing the effectiveness of a projection-based approximation algorithm, are also presented.

eess.SY↗