Finite-Time [Formula: see text] Asynchronous Control for Nonlinear Markov Jump Distributed Parameter Systems via Quantized Fuzzy Output-Feedback Approach

This article focuses on the asynchronous output-feedback control design for a class of nonlinear Markov jump distributed parameter systems based on a hidden Markov model. Initially, the considered systems are represented by a Takagi-Sugeno fuzzy model via a sector nonlinearity approach. Furthermore, asynchronous quantizers are introduced to save the limited communication resource in engineering applications. Then, based on the Lyapunov direct method and some inequality techniques, a series of novel stability criteria, which guarantee the finite-time boundedness and [Formula: see text] disturbance attenuation performance of the target plants, is established in the form of spatial differential linear matrix inequalities. Finally, a simulation study is provided to verify the viability of the developed approach.

Boundary Control of 2-D Burgers' PDE: An Adaptive Dynamic Programming Approach

In this paper, an adaptive dynamic programming-based near optimal boundary controller is developed for partial differential equations (PDEs) modeled by the uncertain Burgers' equation under Neumann boundary condition in 2-D. Initially, Hamilton-Jacobi-Bellman equation is derived in infinite-dimensional space. Subsequently, a novel neural network (NN) identifier is introduced to approximate the nonlinear dynamics in the 2-D PDE. The optimal control input is derived by online estimation of the value function through an additional NN-based forward-in-time estimation and approximated dynamic model. Novel update laws are developed for estimation of the identifier and value function online. The designed control policy can be applied using a finite number of actuators at the boundaries. Local ultimate boundedness of the closed-loop system is studied in detail using Lyapunov theory. Simulation results confirm the optimizing performance of the proposed controller on an unstable 2-D Burgers' equation.

Design of a neural network adaptive controller via a constrained invariant ellipsoids technique

In safety critical applications, control architectures based on adaptive neural networks (NNs) must satisfy strict design specifications. This paper presents a practical approach for designing a mixed linear/adaptive model reference controller that recovers the performance of a reference model, and guarantees the boundedness of the tracking error within an a priori specified compact domain, in the presence of bounded uncertainties. The linear part of the controller results from the solution of an optimization problem where specifications are expressed as linear matrix inequality constraints. The linear controller is then augmented with a general adaptive NN that compensates for the uncertainties. The only requirement for the NN is that its output must be confined within pre-specified saturation limits. Toward this end a specific NN output confinement algorithm is proposed in this paper. The main advantages of the proposed approach are that requirements in terms of worst-case performance can be easily defined during the design phase, and that the design of the adaptation mechanism is largely independent from the synthesis of the linear controller. A numerical example is used to illustrate the design methodology.

Adaptive neural control design for nonlinear distributed parameter systems with persistent bounded disturbances

In this paper, an adaptive neural network (NN) control with a guaranteed L(infinity)-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L(infinity)-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L(infinity)-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(infinity)-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L(infinity)-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.