In this paper, we synthesize controllers for linear time-invariant (LTI) systems using collected offline data. We first synthesize control-invariant sets from offline collected data using backward reachable set computations and then propose a data-driven predictive controller equipped with terminal constraints. After formulating the optimal control problem and designing the terminal constraints and costs, we ensure the recursive feasibility of the optimization problem, asymptotic stability of the closed-loop system, and satisfaction of input and state constraints. We develop an overall online algorithm for our approach that does not require the initial state to be included in the control invariant set, guarantees optimal behavior of the system’s operation, and does not have Lyapunov constraints that restrict the feasibility region. Furthermore, we extend our developed data-driven control algorithm to stabilize interconnected systems in a decentralized manner, where the satisfaction of a small gain condition is additionally required. We illustrate the effectiveness of our approach through a detailed example.

We consider the problem of designing controllers based on measurements affected by noise, for linear systems with unknown dynamics, that ensures one or more performance specifications. In particular, we consider (i) the$\mathcal{D}-\mathbf{stabilization}$problem, where performance specifications are given in terms of placing the eigenvalues of the closed-loop system in a predefined region$\mathcal{D}$of the complex plane, (ii)$\mathcal{H}_{\infty}$performance, (iii)$\mathcal{H}_{2}$performance, and a combination of some of the above. For$\mathcal{D}- \mathbf{stabilization}$problem, a general convex region$\mathcal{D}$defined by a quadratic matrix inequality (QMI) is considered. For this general region$\mathcal{D}$, we provide sufficient conditions, given in terms of data-based linear matrix inequalities, for controller design. For some regions of practical interest, these conditions are necessary and sufficient. We further consider the problem of designing data-driven controllers such that multiple performance specifications, not necessarily given in terms of stability regions, are guaranteed.