Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through trial-and-error. However, the data-based approach notorious not guaranteeing stability, which most fundamental property any system. In this paper, classic Lyapunov’s me...

in this paper, the problem of decentralized model reference adaptive control (mrac) for a class of large scale systems with time varying delay in interconnected term and input and state delays is studied. to compensate the effect of input delay indirectly, a smith predictor built on. to handle the effects of the time delays in input, the adaptive controller part includes two auxiliary dynamic f...

Abstract This paper introduces a distributed observer‐based emotional command‐filtered backstepping (DOECFB) approach for leader‐following cooperative output‐feedback control of heterogenous strict‐feedback multi‐agent systems (MAS) under mismatched uncertainties and input saturation. A novel state observer is designed based on radial‐basis neural networks (RBENNs) that approximate model dynami...

Adaptive control is essential and effective for reliable quadrotor operations in the presence of uncertain modeling parameters unknown time-delayed inputs. This paper presents an original radial basis function neural network-based adaptive fractional-order backstepping controller (RBF-ADFOBC). The nonlinearity inputs eliminated by introducing augmented state variable via Pade’s approximation me...

We study the global existence of classical solutions to volume–surface reaction–diffusion systems with control mass. Such appear naturally from modeling evolution concentrations or densities appearing both in a volume domain and its surface, therefore have attracted considerable attention. Due characteristic coupling, general is challenging issue. In particular, duality method, which powerful d...

Our main result is a strong boundedness result for the class of separable Rosenthal compacta (that is, separable compact subsets of the first Baire class – see [ADK] and [Ro2]) on the Cantor set having a uniformly bounded dense sequence of continuous functions. We shall denote this class by SRC. The phenomenon of strong boundedness, which was first touched by A. S. Kechris and W. H. Woodin in [...

In the monograph [2], the authors define the operator spectrum σ op (A) of a band-dominated operator A (these terms are defined below) and prove that A is Fredholm if and only if all of the operators in σ op (A) are invertible with uniformly bounded inverses. They also ask whether the uniform boundedness condition can in fact be dispensed with. In this note we answer this question affirmatively.

(an Abel equation in canonical form, see [1, p. 24]) is a useful instrument to display rich qualitative properties such as extendability and finite escape time, stability and instability, boundedness, and periodicity. We show the following: (a) The equation has a unique solution that is defined on (−∞,∞). This solution is periodic. (b) As t increases, each solution is attracted into the strip |...

In this paper, interpolating curve or surface with linear inequality constraints is considered as a general convex optimization problem in a Reproducing Kernel Hilbert Space. We propose a new approximation method based on a discretized optimization problem in a finite-dimensional Hilbert space under the same set of constraints. We prove that the approximate solution converges uniformly to the o...