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We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
This paper investigates the output feedback stabilization of parabolic equation with Lipschitz nonlinearity over general multidimensional domain using spectral geometry theories. First, a novel nonlinear observer is designed, and the error…
This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuous-time system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the…
When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the…
We consider discrete ensembles of linear, scalar control systems with single-inputs. Assuming that all the individual systems are unstable, we investigate whether there exist linear feedback control laws that can asymptotically stabilize…
This paper introduces an analytical framework for the derivation of hybrid equations of motion of a flexible quadrotor. This approach helps obtain rigid and elastic equations of motion simultaneously, in a decoupled form, which facilitates…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…
Stability plays a central role in arithmetic. In this article, we explain some basic ideas and present certain constructions for such studies. There are two aspects: namely, general Class Field Theories for Riemann surfaces using…
Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
We present a framework of sequential action control (SAC) for stabilization of systems of partial differential equations which can be posed as abstract semilinear control problems in Hilbert spaces. We follow a late-lumping approach and…
Asymptotic stability in economic receding horizon control can be obtained under a strict dissipativity assumption, related to positive-definiteness of a so-called rotated cost, and through the use of suitable terminal cost and constraints.…
This is a draft paper originally posted on Arxiv as a documentation of a plenary lecture at CDC2023. The core material has been accepted for publication at L4DC 2024. Certainty equivalence adaptive controllers are analysed using a…
The Riccati equation method is used to establish a new stability criteria for linear systems of ordinary differential equations. Two examples are presented in which the obtained result is compared with the results obtained by the Lyapunov…