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We consider the application of Runge-Kutta (RK) methods to gradient systems $(d/dt)x = -\nabla V(x)$, where, as in many optimization problems, $V$ is convex and $\nabla V$ (globally) Lipschitz-continuous with Lipschitz constant $L$.…
Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann--Liouville derivatives is…
This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized…
In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is…
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results…
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…
A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time-invariant systems is proposed. Such an approach is based on the direct self-tuning regulators design framework and the exponentially stable…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…
The paper is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system…
This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization,…
This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…
The discrete-time robust repetitive control (RC, or repetitive controller, also designated RC) problem for nonlinear systems is both challenging and practical. This paper proposes a discrete-time output-feedback RC design for a class of…
We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is colored and dependent across samples. The algorithm, coined…
Due to their relevance in systems analysis and (robust) controller design, we consider the problem of determining control-theoretic system properties of an a priori unknown system from data only. More specifically, we introduce a necessary…
We introduce a novel data-driven method to mitigate the risk of cascading failures in delayed discrete-time Linear Time-Invariant (LTI) systems. Our approach involves formulating a distributionally robust finite-horizon optimal control…
In this paper, we investigate the optimal output tracking problem for linear discrete-time systems with unknown dynamics using reinforcement learning and robust output regulation theory. This output tracking problem only allows to utilize…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…