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In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…
We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm…
We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
This paper proposes a reinforcement learning (RL) algorithm for infinite horizon $\rm {H_{2}/H_{\infty}}$ problem in a class of stochastic discrete-time systems, rather than using a set of coupled generalized algebraic Riccati equations…
This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear…
This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC)…
This work analyzes how the trade-off between the modeling error, the terminal value function error, and the prediction horizon affects the performance of a nominal receding-horizon linear quadratic (LQ) controller. By developing a novel…
In this study, we consider the infinite-horizon, discounted cost, optimal control of stochastic nonlinear systems with separable cost and constraints in the state and input variables. Using the linear-time Legendre transform, we propose a…
In this paper, we develop a provably correct optimal control strategy for a finite deterministic transition system. By assuming that penalties with known probabilities of occurrence and dynamics can be sensed locally at the states of the…
We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based…
We present a quantum algorithm for solving the finite-horizon discrete-time Linear Quadratic Gaussian (LQG) control problem, which integrates optimal control and state estimation in the presence of stochastic disturbances and noise.…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
Markov control algorithms that perform smooth, non-greedy updates of the policy have been shown to be very general and versatile, with policy gradient and Expectation Maximisation algorithms being particularly popular. For these algorithms,…
This paper is concerned with the analysis of the $L_p\ (p\in[1,\infty), p=\infty)$ induced norms of continuous-time linear systems where input signals are restricted to be nonnegative. This norm is referred to as the $L_{p+}$ induced norm…
In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the…
This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
The Receding Horizon Control (RHC) strategy consists in replacing an infinite-horizon stabilization problem by a sequence of finite-horizon optimal control problems, which are numerically more tractable. The dynamic programming principle…