This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or only partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and ii) the cost of the optimization problem -which models control objectives associated with inputs and states of the system -is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of robotics and control of epidemics.

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This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and, ii) the cost of the optimization problem -which models control objectives associated with inputs and states of the system -is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of control of epidemics.

This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller -based on gradient flow dynamics -that (i) is augmented with learning methods to estimate the cost function based on infrequent (and possibly noisy) functional evaluations; and, concurrently, (ii) is designed to drive the inputs and outputs of the dynamical system to the optimizer of the problem. We derive sufficient conditions on the learning error and the controller gain to ensure that the error between the optimizer of the problem and the state of the closed-loop system is ultimately bounded; the error bound accounts for the functional estimation errors and the temporal variability of the unknown disturbance affecting the linear dynamical system. Our results directly lead to exponential input-to-state stability of the closed-loop system. The proposed method and the theoretical bounds are validated numerically.