Search

This article studies the problem of prescribed‐time constrained tracking control for a class of 2×2$$ 2\times 2 $$ hyperbolic partial differential equation (PDE) systems with actuator dynamics, which are described by a set of nonlinear ordinary differential equations (ODEs). Since the control input only appears in the ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite challenging. The most important is that for the control of such ODE controlled PDE systems we mainly make the following two contributions: (1) the controlled output of the PDE system tracks the reference signal within the prescribed time; (2) the controlled output and all the actuator states are constrained. It is the first time that such a prescribed‐time constrained tracking control problem is addressed for the PDE‐ODE coupled system considered in this article. Through rigorous theoretical proof, it is demonstrated that all the system states and control signals are bounded and sufficiently continuous by configuring appropriate design parameters. Finally, the performance is investigated via numerical simulation. [ABSTRACT FROM AUTHOR]

This work develops a network of adaptive boundary observers and studies the agreement between state and parameter estimates for a single target parabolic partial differential equation (PDE) system in the presence of structured and unstructured uncertainties. It is assumed that the unknown parameters take the form of either a structured uncertainty with unknown constant parameters or an unstructured uncertainty that can be neutralized by a radial basis function neural networks with unknown weights. The proposed adaptive observers consisting of m$$ m $$ agents in the network follow the structure of adaptive identifiers for the considered target PDE systems with the insertion of a penalty term in both the state and parameter estimates. Different from earlier efforts, the proposed adaptive laws include a penalty term of the mismatch between the parameter and state estimates generated by the other adjacent agents, which helps to accelerate the estimation of uncertainties. Additionally, the effects of these modifications on the agreement amongst the state and parameter estimates are investigated. Theoretical proofs are provided to show that the proposed approach guarantees the exponential convergence of estimation errors in the case of structured uncertainties and the ultimate boundedness of estimation errors in the case of unstructured uncertainties. Finally, numerical simulations are carried out to verify the effectiveness of the design methods. [ABSTRACT FROM AUTHOR]