Related papers: The Adaptive LQ Regulator
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…
A linear control system with quadratic cost functional over infinite time horizon is considered without assuming controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state…
We propose a new risk-constrained formulation of the classical Linear Quadratic (LQ) stochastic control problem for general partially-observed systems. Our framework is motivated by the fact that the risk-neutral LQ controllers, although…
The closed-loop stability and infinite-horizon performance of receding-horizon approximations are studied for non-stationary linear-quadratic regulator (LQR) problems. The approach is based on a lifted reformulation of the optimal control…
This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the…
The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR)…
Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
The problem of suboptimality under bounded disturbances for the adaptive systems based on speed-graadient approach is discussed. A formulation of the estimated optimality of nonlinear nonlinearly parametrized adaptive control systems is…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of…
This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…
We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…
In this paper we study the optimality of the certainty equivalence approximation in robust finite-horizon optimization problems with expected cost. We provide an algorithm for determining the subset of the state-space for which the…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work…
We study deterministic, discrete linear time-invariant systems with infinite-horizon discounted quadratic cost. It is well-known that standard stabilizability and detectability properties are not enough in general to conclude stability…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…
This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved…