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This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
The concept of Deadbeat Robust Model Predictive Control (DRMPC) is to completely extinguish the effect of external disturbances within the first few steps of the prediction horizon. The benefit is that the remaining dynamics of the system…
Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system.…
In this technical note, we study the mean square stability-based analysis of stochastic continuous-time linear networked systems. The stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output…
This paper presents a linear-programming based algorithm to perform data-driven stabilizing control of linear positive systems. A set of state-input-transition observations is collected up to magnitude-bounded noise. A state feedback…
Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using…
Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…
Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control…
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however…
This paper proposes a novel hybrid control framework for switched linear parameter-varying (LPV) systems under hysteresis switching logic. By introducing a controller state-reset mechanism, the hybrid LPV synthesis problem is reformulated…