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

Minimax Adaptive Estimation for Finite Sets of Linear Systems

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained quadratic programming. The estimator tends to learn the dynamics of the system, and once the uncertain parameters have been sufficiently estimated, the estimator behaves like a standard Kalman filter.Comment: Accompanying code: https://github.com/kjellqvist/MinimaxEstimation.j

Laguerre Bases for Youla-Parametrized Optimal-Controller Design: Numerical Issues and Solutions

This thesis concerns the evaluation of cost functionals on H2 when designing optimal controllers using finite Youla parameterizations and convex optimization. We propose to compute inner products of stable, strictly proper systems via solving Sylvester equations. The properties of different state space realizations of Laguerre filters, when performing Ritz expansions of the optimal controller are discussed, and a closed form expression of the output orthogonal realization is presented. An algorithm to exploit Toeplitz substructure when solving Lyapunov equations is discussed, and a method to extend SISO results to MIMO systems using the vectorization operator is proposed. Finally the methods are evaluated on example systems from the industry, where it is shown that properly selecting the cutoff frequency of the filters is an important problem that should be discussed when Laguerre bases are used to parametrize the optimal controller

Laguerre Bases for Youla-Parametrized Optimal-Controller Design: Numerical Issues and Solutions

This thesis concerns the evaluation of cost functionals on H2 when designing optimal controllers using finite Youla parameterizations and convex optimization. We propose to compute inner products of stable, strictly proper systems via solving Sylvester equations. The properties of different state space realizations of Laguerre filters, when performing Ritz expansions of the optimal controller are discussed, and a closed form expression of the output orthogonal realization is presented. An algorithm to exploit Toeplitz substructure when solving Lyapunov equations is discussed, and a method to extend SISO results to MIMO systems using the vectorization operator is proposed. Finally the methods are evaluated on example systems from the industry, where it is shown that properly selecting the cutoff frequency of the filters is an important problem that should be discussed when Laguerre bases are used to parametrize the optimal controller

Learning-Enabled Robust Control with Noisy Measurements

We present a constructive approach to bounded l2-gain adaptive control with noisy measurements for linear time-invariant scalar systems with uncertain parameters belonging to a finite set. The gain bound refers to the closed-loop system, including the learning procedure. The approach is based on forward dynamic programming to construct a finite-dimensional information state consisting of H-infinity-observers paired with a recursively computed performance metric. We do not assume prior knowledge of a stabilizing controller

On Infinite-horizon System Level Synthesis Problems

System level synthesis is a promising approach that formulates structured optimal controller synthesis problems as convex problems. This work solves the distributed linear-quadratic regulator problem under communication constraints directly in infinite-dimensional space, without the finite-impulse response relaxation common in related work. Our method can also be used to construct optimal distributed Kalman filters with limited information exchange. We combine the distributed Kalman filter with state-feedback control to perform localized LQG control with communication constraints. We provide agent-level implementation details for the resulting output-feedback state-space controller

Minimax Adaptive Estimation for Finite Sets of Linear Systems

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely eterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained quadratic programming. The estimator tends to learn the dynamics of the system, and once the uncertain parameters have been sufficiently estimated, the estimator behaves like a standard Kalman filter

Learning Optimal Team-Decisions

In this paper, we linear quadratic team decision problems, where a team of agents minimizes a convex quadratic cost function over T time steps subject to possibly distinct linear measurements of the state of nature. We assume that the state of nature is a Gaussian random variable and that the agents do not know the cost function nor the linear functions mapping the state of nature to their measurements. We present a gradient-descent based algorithm with an expected regret of O(log(T)) for full information gradient feedback and O(√(T)) for bandit feedback. In the case of bandit feedback, the expected regret has an additional multiplicative term O(d) where d reflects the number of learned parameters

Numerical Pitfalls in Q-Design

Q-design is a powerful method for designing approximately optimal LTI controllers and assessing the achievable control performance. Unfortunately, numerical issues are often encountered in Q-design which limits its applicability. This paper warns about two numerical pitfalls in Q-design when using H 2 costs and Laguerre-type basis functions