Data-driven control via Petersen’s lemma

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen’s lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen’s lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through alternate (convex) sum-of-squares programs. The findings are illustrated numerically

Robust Quasi-LPV Controller Design via Integral Quadratic Constraint Analysis

Reduced cost of sensors and increased computing power is enabling the development and implementation of control systems that can simultaneously regulate multiple variables and handle conflicting objectives while maintaining stringent performance objectives. To make this a reality, practical analysis and design tools must be developed that allow the designer to trade-off conflicting objectives and guarantee performance in the presence of uncertain system dynamics, an uncertain environment, and over a wide range of operating conditions. As a first step towards this goal, we organize and streamline a promising robust control approach, Robust Linear Parameter Varying control, which integrates three fields of control theory: Integral Quadratic Constraints (IQC) to characterize uncertainty and nonlinearities, Linear Parameter Varying systems (LPV) that formalizes gain-scheduling, and convex optimization to solve the resulting robust control Linear Matrix Inequalities (LMI). To demonstrate the potential of this approach, it was applied to the design of a robust linear parametrically varying controller for an ecosystem with nonlinear predator-prey-hunter dynamics

Adaptive Output Feedback Control of Nonlinear Systems

Adaptive output feedback control of classes of nonlinear systems and related problems are investigated. The classes of systems that are studied include Lipschitz nonlinear systems, large-scale interconnected nonlinear systems with quadratically bounded interconnections, nonlinear systems containing product terms of unmeasured states and unknown parameters, and mechanical systems with unknown time-varying parameters and disturbances. Solutions and their bounds of relevant algebraic and differential matrix equations in systems and control theory are also studied. For analysis and synthesis of controllers, methods from Lyapunov theory, Algebraic Riccati Equations (AREs), Linear Matrix Inequalities (LMIs), and local polynomial approximations are extensively used. Findings and Conclusions: A stable output feedback controller can be designed for Lipschitz nonlinear systems if sufficient conditions related to distances to uncontrollability and unobservability of pairs of system matrices are satisfied. Stable linear decentralized output feedback controllers can be designed for large-scale systems if certain sufficient conditions are satisfied; these conditions can be formulated either as existence of positive definite solutions to AREs or as a feasibility problem of an LMI. By casting the dynamics of a nonlinear system, which contains products of unmeasurable states and unknown parameters, into a modified form, a stable adaptive output feedback controller can be constructed using a parameter dependent Lyapunov function; the procedure for casting the system dynamics into a modified form is constructive and is always possible. A stable adaptive controller for mechanical systems with unknown time-varying parameters and disturbances can be designed using local polynomial approximation; the time-varying parameters and disturbances are estimated by a modified least-squares algorithm using a new resetting strategy, which is a consequence of keeping the estimates continuous at the beginning of each time interval of local polynomial approximation. For all the problems that are investigated, simulation and experimental results are given to verify and validate the proposed methods.Department of Biochemistry and Molecular Biolog