arXiv subjects

Ali Pakniyat

Publications and source records attributed to Ali Pakniyat.

14 recordsLinked to original sources

arXiv2026

Hybrid Optimal Control of Homogeneous Epidemiological Compartmental Models with Regime Switching

Optimal intervention design is formulated as a hybrid optimal control problem for multiphase homogeneous epidemiological systems. The system extends a foundational compartmental model through intermediate phases that incorporate work-from-home (WFH) policies and a vaccination protocol, yielding a four-phase hybrid system that captures policy escalation and relaxation. Key characteristics of the resulting hybrid system include (i) phase-dependent continuous dynamics and running costs that respectively capture distinct disease transmission mechanisms and shifting public health socioeconomic trade-offs, (ii) a combination of autonomous and controlled switchings for intervention policies, whose times are co-optimized - whether indirectly via state thresholds or directly as decision variables alongside continuous inputs to minimize the overall cost, and (iii) nontrivial state jump maps that govern transitions between phases with differing state and control space dimensions. The Hybrid Minimum Principle (HMP) is invoked to obtain the optimal solutions. Numerical results demonstrate that coordinating WFH policies with vaccination efforts provides improved mitigation of disease spread compared to single-phase policy interventions.

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arXiv2026

Nonlinear Stochastic Optimal Control and Optimal Stopping using the Fokker-Planck Transformation

In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent diffusion, we rewrite the controlled Fokker-Planck equation as a continuity equation driven by a score-corrected velocity field, yielding a deterministic characteristic dynamics that reproduces the marginal law of the stochastic system. Leveraging Stein-type identities, we show that the associated distributional dynamic programming equation admits the same second-order differential operator as the distributional stochastic Hamilton-Jacobi-Bellman formulation. Building on this representation, we formulate an optimal control problem with state-dependent terminal-time assignment and terminal distributional constraints and derive the first-order necessary conditions using variational analysis. We present the conditions both for a common terminal time and for the general case of state-dependent stopping.

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arXiv2026

Tube-Based Safety for Anticipative Tracking in Multi-Agent Systems

A tube-based safety framework is presented for robust anticipative tracking in nonlinear Brunovsky multi-agent systems subject to bounded disturbances. The architecture establishes robust safety certificates for a feedforward-augmented ancillary control policy. By rendering the state-deviation dynamics independent of the agents' internal nonlinearities, the formulation strictly circumvents the restrictive Lipschitz-bound feasibility conditions otherwise required for robust stabilization. Consequently, this structure admits an explicit, closed-form robust positively invariant (RPI) tube radius that systematically attenuates the exponential control barrier function (eCBF) tightening margins, thereby mitigating constraint conservatism while preserving formal forward invariance. Within the distributed model predictive control (MPC) layer, mapping the local tube radii through the communication graph yields a closed-form global formation error bound formulated via the minimum singular value of the augmented Laplacian. Robust inter-agent safety is enforced with minimal communication overhead, requiring only a single scalar broadcast per neighbor at initialization. Numerical simulations confirm the framework's efficacy in safely navigating heterogeneous formations through cluttered environments.

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arXiv2025

Robust Multi-Agent Safety via Tube-Based Tightened Exponential Barrier Functions

This paper presents a constructive framework for synthesizing provably safe controllers for nonlinear multi-agent systems subject to bounded disturbances. The methodology applies to systems representable in Brunovsky canonical form, accommodating arbitrary-order dynamics in multi-dimensional spaces. The central contribution is a method of constraint tightening that formally couples robust error feedback with nominal trajectory planning. The key insight is that the design of an ancillary feedback law, which confines state errors to a robust positively invariant (RPI) tube, simultaneously provides the exact information needed to ensure the safety of the nominal plan. Specifically, the geometry of the resulting RPI tube is leveraged via its support function to derive state-dependent safety margins. These margins are then used to systematically tighten the high relative-degree exponential control barrier function (eCBF) constraints imposed on the nominal planner. This integrated synthesis guarantees that any nominal trajectory satisfying the tightened constraints corresponds to a provably safe trajectory for the true, disturbed system. We demonstrate the practical utility of this formal synthesis method by implementing the planner within a distributed Model Predictive Control (MPC) scheme, which optimizes performance while inheriting the robust safety guarantees.

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arXiv2025

Distributed Leader-Follower Consensus for Uncertain Multiagent Systems with Time-Triggered Switching of the Communication Network

A distributed adaptive control strategy is developed for heterogeneous multiagent systems in nonlinear Brunovsky form with ${\pd}$-dimensional $n^{\text{th}}$-order dynamics, operating under time-triggered switching communication topologies. The approach uses repulsive potential functions to ensure agent-agent and obstacle safety, while neural network estimators compensate for system uncertainties and disturbances. A high-order control barrier function framework is then employed to certify the positive invariance of the safe sets and the boundedness of the proposed control inputs. The resulting distributed control and adaptive laws, together with dwell-time requirements for topology transitions, achieve leader-following consensus. This integrated design provides synchronized formation and robust disturbance rejection in evolving network configurations, and its effectiveness is demonstrated through numerical simulations.

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arXiv2025

A Time-Reversal Control Synthesis for Steering the State of Stochastic Systems

This paper presents a novel approach for steering the state of a stochastic control-affine system to a desired target within a finite time horizon. Our method leverages the time-reversal of diffusion processes to construct the required feedback control law. Specifically, the control law is the so-called score function associated with the time-reversal of random state trajectories that are initialized at the target state and are simulated backwards in time. A neural network is trained to approximate the score function, enabling applicability to both linear and nonlinear stochastic systems. Numerical experiments demonstrate the effectiveness of the proposed method across several benchmark examples.

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arXiv2024

Distributed Adaptive Consensus with Obstacle and Collision Avoidance for Networks of Heterogeneous Multi-Agent Systems

This paper presents a distributed adaptive control strategy for multi-agent systems with heterogeneous dynamics and collision avoidance. We propose an adaptive control strategy designed to ensure leader-following formation consensus while effectively managing collision and obstacle avoidance using potential functions. By integrating neural network-based disturbance estimation and adaptive tuning laws, the proposed strategy ensures consensus and stability in leader-following formations under fixed topologies.

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arXiv2022

Solving Feynman-Kac Forward Backward SDEs Using McKean-Markov Branched Sampling

We propose a new method for the numerical solution of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. Using Girsanov's change of probability measures, it is demonstrated how a McKean-Markov branched sampling method can be utilized for the forward integration pass, as long as the controlled drift term is appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of a space-filling tree consisting of trajectory samples. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method is developed to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories. The proposed methodology is numerically demonstrated on linear and nonlinear stochastic optimal control problems with non-quadratic running costs, which reveal significant convergence improvements over previous FBSDE-based numerical solution methods.

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arXiv2022

Shaping Large Population Agent Behaviors Through Entropy-Regularized Mean-Field Games

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time setting. We show that entropy regularization provides the necessary regularity conditions, that are lacking in the standard finite mean field games. Such regularity conditions enable us to design fixed-point iteration algorithms to find the unique mean-field equilibrium (MFE). Furthermore, the reference policy used in the regularization provides an extra parameter, through which one can control the behavior of the population. We first consider a stochastic game with a large population of $N$ homogeneous agents. We establish conditions for the existence of a Nash equilibrium in the limiting case as $N$ tends to infinity, and we demonstrate that the Nash equilibrium for the infinite population case is also an $ε$-Nash equilibrium for the $N$-agent system, where the sub-optimality $ε$ is of order $\mathcal{O}\big(1/\sqrt{N}\big)$. Finally, we verify the theoretical guarantees through a resource allocation example and demonstrate the efficacy of using a reference policy to control the behavior of a large population.

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arXiv2021

Value Function Estimators for Feynman-Kac Forward-Backward SDEs in Stochastic Optimal Control

Two novel numerical estimators are proposed for solving forward-backward stochastic differential equations (FBSDEs) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. In contrast to the current numerical approaches which are based on the discretization of the continuous-time FBSDE, we propose a converse approach, namely, we obtain a discrete-time approximation of the on-policy value function, and then we derive a discrete-time estimator that resembles the continuous-time counterpart. The proposed approach allows for the construction of higher accuracy estimators along with error analysis. The approach is applied to the policy improvement step in reinforcement learning. Numerical results and error analysis are demonstrated using (i) a scalar nonlinear stochastic optimal control problem and (ii) a four-dimensional linear quadratic regulator (LQR) problem. The proposed estimators show significant improvement in terms of accuracy in both cases over Euler-Maruyama-based estimators used in competing approaches. In the case of LQR problems, we demonstrate that our estimators result in near machine-precision level accuracy, in contrast to previously proposed methods that can potentially diverge on the same problems.

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arXiv2021

Forward-Backward Rapidly-Exploring Random Trees for Stochastic Optimal Control

We propose a numerical method for the computation of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. By the use of the Girsanov change of probability measures, it is demonstrated how a rapidly-exploring random tree (RRT) method can be utilized for the forward integration pass, as long as the controlled drift terms are appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of the constructed RRT. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method is developed to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories. The results of the proposed methodology are demonstrated on linear and nonlinear stochastic optimal control problems with non-quadratic running costs, which reveal significant convergence improvements over previous FBSDE-based numerical solution methods.

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arXiv2018

A Class of Hybrid LQG Mean Field Games with State-Invariant Switching and Stopping Strategies

A novel framework is presented that combines Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory to obtain a unique $\epsilon$-Nash equilibrium for a non-cooperative game with switching and stopping times. We consider the case where there exists one major agent with a significant influence on the system together with a large number of minor agents constituting two subpopulations, each agent with individually asymptotically negligible effect on the whole system. Each agent has stochastic linear dynamics with quadratic costs, and the agents are coupled in their dynamics and costs by the average state of minor agents (i.e. the empirical mean field). It is shown that for a class of Hybrid LQG MFGs, the optimal switching and stopping times are state-invariant and only depend on the dynamical parameters of each agent. Accordingly, a hybrid systems formulation of the game is presented via the indexing by discrete events: (i) the switching of the major agent between alternative dynamics or (ii) the termination of the agents' trajectories in one or both of the subpopulations of minor agents. Optimal switchings and stopping time strategies together with best response control actions for, respectively, the major agent and all minor agents are established with respect to their individual cost criteria by an application of Hybrid LQG MFG theory.

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arXiv2018

On the Hybrid Minimum Principle

The Hybrid Minimum Principle (HMP) is established for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied by changes in the dimension of the state space. First order variational analysis is performed via the needle variation methodology and the necessary optimality conditions are established in the form of the HMP. A feature of special interest in this work is the explicit presentations of boundary conditions on the Hamiltonians and the adjoint processes before and after switchings and jumps. In addition to an analytic example, the HMP results are illustrated for the optimal control of an electric vehicle with transmission, where the modelling of the powertrain requires the consideration of both autonomous and controlled switchings accompanied by dimension changes.

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arXiv2016

On the Relation between the Minimum Principle and Dynamic Programming for Classical and Hybrid Control Systems

Hybrid optimal control problems are studied for a general class of hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and in addition to terminal and running costs switching between discrete states incurs costs. The statements of the Hybrid Minimum Principle and Hybrid Dynamic Programming are presented in this framework and it is shown that under certain assumptions the adjoint process in the Hybrid Minimum Principle and the gradient of the value function in Hybrid Dynamic Programming are governed by the same set of differential equations and have the same boundary conditions and hence are almost everywhere identical to each other along optimal trajectories. Analytic examples are provided to illustrate the results and, in particular, a Riccati formalism for linear quadratic hybrid tracking problems is presented.

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