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This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem…
In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it…
We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential equations and integral equations, commonly used in fluid…
We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations ($\Htwo,\Hinf,\LQR$) and previous works…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
This paper presents a robust control synthesis and analysis framework for nonlinear systems with uncertain initial conditions. First, a deep learning-based lifting approach is proposed to approximate nonlinear dynamical systems with linear…
A system of plane curves defined by prescribing n points of multiplicity m in general position is regular if n > (2m)^2. The proof uses computation of limits of linear systems acquiring fixed divisors, an interesting problem in itself.
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
This paper studies the stabilization for a kind of linear and impulse control systems in finite-dimensional spaces, where impulse instants appear periodically. We present several characterizations on the stabilization; show how to design…
The feedback linearization method is further developed for the controller design on general nonlinear systems. Through the Lyapunov stability theory, the intractable nonlinear implicit algebraic control equations are effectively solved, and…
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
This paper discusses the stability analysis of linear parameter varying systems with a parameter-dependent delay where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. Based on stochastic…
In this paper, we propose a novel dynamic state-feedback controller for polytopic linear parameter-varying (LPV) systems with constant input matrix. The controller employs a projected gradient flow method to continuously improve its control…
Model mismatch often poses challenges in model-based controller design. This paper investigates model predictive control (MPC) of uncertain linear systems with input constraints, focusing on stability and closed-loop infinite-horizon…
In this paper, we consider the problem of input-output linearization of the longitudinal flight dynamics. In longitudinal flight dynamics, inputs are typically thrust and elevator deflection whereas the outputs are the velocity and the…
The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs…