Stochastic optimal adaptive controller and communication protocol design for networked control systems

Networked Control System (NCS) is a recent topic of research wherein the feedback control loops are closed through a real-time communication network. Many design challenges surface in such systems due to network imperfections such as random delays, packet losses, quantization effects and so on. Since existing control techniques are unsuitable for such systems, in this dissertation, a suite of novel stochastic optimal adaptive design methodologies is undertaken for both linear and nonlinear NCS in presence of uncertain system dynamics and unknown network imperfections such as network-induced delays and packet losses. The design is introduced in five papers. In Paper 1, a stochastic optimal adaptive control design is developed for unknown linear NCS with uncertain system dynamics and unknown network imperfections. A value function is adjusted forward-in-time and online, and a novel update law is proposed for tuning value function estimator parameters. Additionally, by using estimated value function, optimal adaptive control law is derived based on adaptive dynamic programming technique. Subsequently, this design methodology is extended to solve stochastic optimal strategies of linear NCS zero-sum games in Paper 2. Since most systems are inherently nonlinear, a novel stochastic optimal adaptive control scheme is then developed in Paper 3 for nonlinear NCS with unknown network imperfections. On the other hand, in Paper 4, the network protocol behavior (e.g. TCP and UDP) are considered and optimal adaptive control design is revisited using output feedback for linear NCS. Finally, Paper 5 explores a co-design framework where both the controller and network scheduling protocol designs are addressed jointly so that proposed scheme can be implemented into next generation Cyber Physical Systems --Abstract, page iv

On Control and Estimation of Large and Uncertain Systems

This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

Regret Minimization in Partially Observable Linear Quadratic Control

We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to design a controller. We propose a novel way to decompose the regret and provide an end-to-end sublinear regret upper bound for partially observable linear quadratic control. Finally, we provide stability guarantees and establish a regret upper bound of O(T^(2/3)) for ExpCommit, where T is the time horizon of the problem