Related papers: Sum-of-Squares approach to feedback control of lam…
The paper presents a nonlinear state-feedback control design approach for long-time average cost control, where the control effort is assumed to be expensive. The approach is based on sum-of-squares and semi-definite programming techniques.…
The two main contributions of this paper are a proof of concept of the recent novel idea in the area of long-time average cost control, and a new method of overcoming the well-known difficulty of non-convexity of simultaneous optimization…
One of the desirable objectives in feedback control design is to formulate and solve the design problem as an optimisation problem that is convex, so that an optimal solution can be found efficiently. Unfortunately many control design…
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 paper we use optimization-based methods to design output-feedback controllers for a class of one-dimensional parabolic partial differential equations. The output may be distributed or point-measurements. The input may be distributed…
Neural network controllers have the potential to improve the performance of feedback systems compared to traditional controllers, due to their ability to act as general function approximators. However, quantifying their safety and…
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned…
This paper presents an approach to systematically design sliding mode control and manifold to stabilize nonlinear uncertain systems. The objective is also accomplished to enlarge the inner bound of region of attraction for closed-loop…
We present a control design procedure for nonlinear control systems in which we represent a potentially high dimensional system with a low dimensional continuous-state abstraction. The abstraction generates a reference which the original…
This work presents a computationally efficient approach to data-driven robust contracting controller synthesis for polynomial control-affine systems based on a sum-of-squares program. In particular, we consider the case in which a system…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of…
The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any…
The control Lyapunov function (CLF) approach to nonlinear control design is well established. Moreover, when the plant is control affine and polynomial, sum-of-squares (SOS) optimization can be used to find a polynomial controller as a…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
Recent advances in learning techniques have enabled the modelling of unknown dynamical systems directly from data. However, in many contexts, these learning-based methods are short of safety guarantee and strict stability verification. To…
We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial…
In this paper, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without…