Related papers: On Approximating Polynomial-Quadratic Regulator Pr…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
This paper presents adaptive robust quadratic program (QP) based control using control Lyapunov and barrier functions for nonlinear systems subject to time-varying and state-dependent uncertainties. An adaptive estimation law is proposed to…
Energy functions offer natural extensions of controllability and observability Gramians to nonlinear systems, enabling various applications such as computing reachable sets, optimizing actuator and sensor placement, performing balanced…
This work has introduced a generalized formulation of the problem of eigenvalue spectrum assignment for block matrix systems. In this problem, it is required to construct a feedback that provides that the matrix of the closed-loop system is…
We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach…
Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
In this work we present a nonlinear adaptive suboptimal control strategy for uncertain nonlinear systems. Stochastic parametric uncertainty is dealt with by employing spectral decomposition of the random variables by means of the…
The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular…
This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller…
A promising method for constructing a data-driven output-feedback control law involves the construction of a model-free observer. The Linear Quadratic Regulator (LQR) optimal control policy can then be obtained by both policy-iteration (PI)…
Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization…
This paper addresses the problem of robust control of a linear discrete-time system subject to bounded disturbances and to measurement and control budget constraints. Using Q-parameterization and a polytope containment method, we prove that…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
We consider the problem of planning under observation and motion uncertainty for nonlinear robotics systems. Determining the optimal solution to this problem, generally formulated as a Partially Observed Markov Decision Process (POMDP), is…
A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows,…
We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control schemes. More recently, for the average…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…