arXiv subjects

Iman Shames

Publications and source records attributed to Iman Shames.

At least 55 records · Page 3Linked to original sources

arXiv2024

Self-Tuning Network Control Architectures with Joint Sensor and Actuator Selection

We formulate a mathematical framework for designing a self-tuning network control architecture, and propose a computationally-feasible greedy algorithm for online architecture optimization. In this setting, the locations of active sensors and actuators in the network, as well as the feedback control policy are jointly adapted using all available information about the network states and dynamics to optimize a performance criterion. We show that the case with full-state feedback can be solved with dynamic programming, and in the linear-quadratic setting, the optimal cost functions and policies are piecewise quadratic and piecewise linear, respectively. Our framework is extended for joint sensor and actuator selection for dynamic output feedback control with both control performance and architecture costs. For large networks where exhaustive architecture search is prohibitive, we describe a greedy heuristic for actuator selection and propose a greedy swapping algorithm for joint sensor and actuator selection. Via numerical experiments, we demonstrate a dramatic performance improvement of greedy self-tuning architectures over fixed architectures. Our general formulation provides an extremely rich and challenging problem space with opportunities to apply a wide variety of approximation methods from stochastic control, system identification, reinforcement learning, and static architecture design for practical model-based control.

eess.SY↗

arXiv2023

On Distributed Nonconvex Optimisation Via Modified ADMM

This paper addresses the problem of nonconvex nonsmooth decentralised optimisation in multi-agent networks with undirected connected communication graphs. Our contribution lies in introducing an algorithmic framework designed for the distributed minimisation of the sum of a smooth (possibly nonconvex and non-separable) function and a convex (possibly nonsmooth and non-separable) regulariser. The proposed algorithm can be seen as a modified version of the ADMM algorithm where, at each step, an "inner loop" needs to be iterated for a number of iterations. The role of the inner loop is to aggregate and disseminate information across the network. We observe that a naive decentralised approach (one iteration of the inner loop) may not converge. We establish the asymptotic convergence of the proposed algorithm to the set of stationary points of the nonconvex problem where the number of iterations of the inner loop increases logarithmically with the step count of the ADMM algorithm. We present numerical results demonstrating the proposed method's correctness and performance.

math.OC↗

arXiv2023

Distributionally Time-Varying Online Stochastic Optimization under Polyak-Łojasiewicz Condition with Application in Conditional Value-at-Risk Statistical Learning

In this work, we consider a sequence of stochastic optimization problems following a time-varying distribution via the lens of online optimization. Assuming that the loss function satisfies the Polyak-Łojasiewicz condition, we apply online stochastic gradient descent and establish its dynamic regret bound that is composed of cumulative distribution drifts and cumulative gradient biases caused by stochasticity. The distribution metric we adopt here is Wasserstein distance, which is well-defined without the absolute continuity assumption or with a time-varying support set. We also establish a regret bound of online stochastic proximal gradient descent when the objective function is regularized. Moreover, we show that the above framework can be applied to the Conditional Value-at-Risk (CVaR) learning problem. Particularly, we improve an existing proof on the discovery of the PL condition of the CVaR problem, resulting in a regret bound of online stochastic gradient descent.

math.OC↗

arXiv2023

Non-uniform Observability for Moving Horizon Estimation and stability with respect to additive perturbation

This paper formalises the concepts of weakly and weakly regularly persistent input trajectory as well as their link to the Observability Grammian and the existence and uniqueness of solutions of Moving Horizon Estimation (MHE) problems. Additionally, thanks to a new time-uniform Implicit Function Theorem, these notions are proved to imply the stability of MHE solutions with respect to small additive perturbation in the measurements and in the dynamics, both uniformly and non-uniformly in time. Finally, examples and counter-examples of weakly persistent and weakly regularly persistent input trajectories are given in the case of 2D bearing-only navigation.

math.OC↗

arXiv2023

Learning Safety Filters for Unknown Discrete-Time Linear Systems

A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and control inputs. The empirically learned model and process noise covariance with their confidence bounds are used to construct a robust optimization problem for minimally modifying nominal control actions to ensure safety with high probability. The optimization problem relies on tightening the original safety constraints. The magnitude of the tightening is larger at the beginning since there is little information to construct reliable models, but shrinks with time as more data becomes available.

cs.LG↗

arXiv2023

Distributed Block Coordinate Moving Horizon Estimation for 2D Visual-Inertial-Odometry SLAM

This paper presents a Visual Inertial Odometry Landmark-based Simultaneous Localisation and Mapping algorithm based on a distributed block coordinate nonlinear Moving Horizon Estimation scheme. The main advantage of the proposed method is that the updates on the position of the landmarks are based on a Bundle Adjustment technique that can be parallelised over the landmarks. The performance of the method is demonstrated in simulations in different environments and with different types of robot trajectory. Circular and wiggling patterns in the trajectory lead to better estimation performance than straight ones, confirming what is expected from recent nonlinear observability theory.

cs.RO↗

arXiv2023

Nonlinear Dual control based on Fast Moving Horizon estimation and Model Predictive Control with an observability constraint

This paper proposes an algorithm that combines Fast Moving Horizon Parameter Estimation and Model Predictive Control subject to an observability constraint designed to ensure a lower bound on the performance of the parameter estimator. Output-feedback stability is proved through input-to-state stability of the state/error system under a small noise and initial error assumption. Numerical experiments have been carried out in the case of Active Simultaneous Localisation and Mapping (SLAM).

math.OC↗

arXiv2023

Regret Analysis of Online LQR Control via Trajectory Prediction and Tracking: Extended Version

In this paper, we propose and analyze a new method for online linear quadratic regulator (LQR) control with a priori unknown time-varying cost matrices. The cost matrices are revealed sequentially with the potential for future values to be previewed over a short window. Our novel method involves using the available cost matrices to predict the optimal trajectory, and a tracking controller to drive the system towards it. We adopted the notion of dynamic regret to measure the performance of this proposed online LQR control method, with our main result being that the (dynamic) regret of our method is upper bounded by a constant. Moreover, the regret upper bound decays exponentially with the preview window length, and is extendable to systems with disturbances. We show in simulations that our proposed method offers improved performance compared to other previously proposed online LQR methods.

math.OC↗

arXiv2023

The graph structure of two-player games

In this paper we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc indicating the preferred option for that player. Response graphs, and particularly their sink strongly connected components, play an important role in modern techniques in evolutionary game theory and multi-agent learning. We show that the response graph is a simple and well-motivated model of strategic interaction which captures many non-trivial properties of a game, despite not depending on cardinal payoffs. We characterise the games which share a response graph with a zero-sum or potential game respectively, and demonstrate a duality between these sets. This allows us to understand the influence of these properties on the response graph. The response graphs of Matching Pennies and Coordination are shown to play a key role in all two-player games: every non-iteratively-dominated strategy takes part in a subgame with these graph structures. As a corollary, any game sharing a response graph with both a zero-sum game and potential game must be dominance-solvable. Finally, we demonstrate our results on some larger games.

cs.GT↗

arXiv2023

The Replicator Dynamic, Chain Components and the Response Graph

In this paper we examine the relationship between the flow of the replicator dynamic, the continuum limit of Multiplicative Weights Update, and a game's response graph. We settle an open problem establishing that under the replicator, sink chain components -- a topological notion of long-run outcome of a dynamical system -- always exist and are approximated by the sink connected components of the game's response graph. More specifically, each sink chain component contains a sink connected component of the response graph, as well as all mixed strategy profiles whose support consists of pure profiles in the same connected component, a set we call the content of the connected component. As a corollary, all profiles are chain recurrent in games with strongly connected response graphs. In any two-player game sharing a response graph with a zero-sum game, the sink chain component is unique. In two-player zero-sum and potential games the sink chain components and sink connected components are in a one-to-one correspondence, and we conjecture that this holds in all games.

cs.GT↗

arXiv2023

Self-Tuning Network Control Architectures

We formulate a general mathematical framework for self-tuning network control architecture design. This problem involves jointly adapting the locations of active sensors and actuators in the network and the feedback control policy to all available information about the time-varying network state and dynamics to optimize a performance criterion. We propose a general solution structure analogous to the classical self-tuning regulator from adaptive control. We show that a special case with full-state feedback can be solved in principle with dynamic programming, and in the linear quadratic setting the optimal cost functions and policies are piecewise quadratic and piecewise linear, respectively. For large networks where exhaustive architecture search is prohibitive, we describe a greedy heuristic for joint architecture-policy design. We demonstrate in numerical experiments that self-tuning architectures can provide dramatically improved performance over fixed architectures. Our general formulation provides an extremely rich and challenging problem space with opportunities to apply a wide variety of approximation methods from stochastic control, system identification, reinforcement learning, and static architecture design.

math.OC↗

arXiv2022

First order online optimisation using forward gradients in over-parameterised systems

The success of deep learning over the past decade mainly relies on gradient-based optimisation and backpropagation. This paper focuses on analysing the performance of first-order gradient-based optimisation algorithms, gradient descent and proximal gradient, with time-varying non-convex cost function under (proximal) Polyak-Łojasiewicz condition. Specifically, we focus on using the forward mode of automatic differentiation to compute gradients in the fast-changing problems where calculating gradients using the backpropagation algorithm is either impossible or inefficient. Upper bounds for tracking and asymptotic errors are derived for various cases, showing the linear convergence to a solution or a neighbourhood of an optimal solution, where the convergence rate decreases with the increase in the dimension of the problem. We show that for a solver with constraints on computing resources, the number of forward gradient iterations at each step can be a design parameter that trades off between the tracking performance and computing constraints.

math.OC↗

arXiv2022

Minimum-Time Escape from a Circular Region for a Dubins Car

We investigate the problem of finding paths that enable a robot modeled as a Dubins car (i.e., a constant-speed finite-turn-rate unicycle) to escape from a circular region of space in minimum time. This minimum-time escape problem arises in marine, aerial, and ground robotics in situations where a safety region has been violated and must be exited before a potential negative consequence occurs (e.g., a collision). Using the tools of nonlinear optimal control theory, we show that a surprisingly simple closed-form feedback control law solves this minimum-time escape problem, and that the minimum-time paths have an elegant geometric interpretation.

eess.SY↗

arXiv2022

MITL Verification Under Timing Uncertainty

A Metric Interval Temporal Logic (MITL) verification algorithm is presented. It verifies continuous-time signals without relying on high frequency sampling. Instead, it is assumed that collections of over- and under-approximating intervals are available for the times at which the individual atomic propositions hold true for a given signal. These are combined inductively to generate corresponding over- and under-approximations for the specified MITL formula. The gap between the over- and under-approximations reflects timing uncertainty with respect to the signal being verified, thereby providing a quantitative measure of the conservativeness of the algorithm. The verification is exact when the over-approximations for the atomic propositions coincide with the under-approximations. Numerical examples are provided to illustrate.

cs.LO↗

arXiv2022

Gradient Free Cooperative Seeking of a Moving Source

In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum seeking with formation control in order to converge to the extrema faster by minimising the gradient estimation error. By formalising the relationship between the formation and the gradient estimation error, we provide a novel analysis to prove the convergence of the network to a bounded neighbourhood of the field's time varying extrema. We assume the time-varying field satisfies the Polyak Lojasiewicz inequality and the gradient is Lipschitz continuous at each iteration. Numerical studies and comparisons are provided to support the theoretical results.

math.OC↗

arXiv2022

A Logistic Regression Approach to Field Estimation Using Binary Measurements

In this letter, we consider the problem of field estimation using binary measurements. Previous work has formulated the problem as a parameter estimation problem, with the parameter estimation carried out in an online manner using sequential Monte Carlo techniques. In the current work, we consider an alternative approach to the parameter estimation based on online logistic regression. The developed algorithm is less computationally intensive than the sequential Monte Carlo approach, while having more reliable estimation performance.

stat.ME↗

arXiv2022

Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise

We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Moreover, the control design method accommodates a highly structured uncertainty representation that can capture uncertainty shape more effectively than existing approaches. We show through numerical experiments that the proposed robust data-driven output feedback controller can significantly outperform a certainty equivalent controller on various measures of sample complexity and stability robustness.

eess.SY↗

arXiv2022

Risk-Bounded Temporal Logic Control of Continuous-Time Stochastic Systems

Motivated by the recent interest in risk-aware control, we study a continuous-time control synthesis problem to bound the risk that a stochastic linear system violates a given specification. We use risk signal temporal logic as a specification formalism in which distributionally robust risk predicates are considered and equipped with the usual Boolean and temporal operators. Our control approach relies on reformulating these risk predicates as deterministic predicates over mean and covariance states of the system. We then obtain a timed sequence of sets of mean and covariance states from the timed automata representation of the specification. To avoid an explosion in the number of automata states, we propose heuristics to find candidate sequences effectively. To execute and check dynamic feasibility of these sequences, we present a sampled-data control technique based on time discretization and constraint tightening that allows to perform timed transitions while satisfying the continuous-time constraints.

eess.SY↗