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This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method…
For solving constrained (pseudo)-monotone variational inequality, we prove that the upper bound of stepsize $\frac{1}{2L}$ established for the Popov's algorithm and the forward-reflected-backward algorithm is tight. For unconstrained case,…
In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed and convex set constraints. We show that the resulting…
We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an…
This paper presents an efficient, offline method to simultaneously synthesize controllers and seek closed-loop Lyapunov functions for constrained piecewise affine systems on triangulated subsets of the admissible states. Triangulation…
We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…
The inherent approximation ability of neural networks plays an essential role in adaptive neural control, where the prerequisite for existence of the compact set is crucial in the control designs. Instead of using practical system state, in…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…
The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be employed to elicit high performance of the Sinc…
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for constructing explicit ranges where quadratic Lyapunov functions…
In this paper, we investigate the model reference adaptive control approach for uncertain piecewise affine systems with performance guarantees. The proposed approach ensures the error metric, defined as the weighted Euclidean norm of the…
We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains…
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…