Related papers: Using dynamic extensions for the backstepping cont…
For the quite extensively developed PDE backstepping methodology for coupled linear hyperbolic PDEs, we provide a generalization from finite collections of such PDEs, whose states at each location in space are vector-valued, to previously…
This work studies the problem of controlling the mean-field density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs…
We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form…
The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear, first-order, hyperbolic systems with non-local terms on bounded domains. It is shown that the emulation design based on…
This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming…
This paper presents bilateral control laws for one-dimensional(1-D) linear 2x2 hyperbolic first-order systems (with spatially varying coefficients). Bilateral control means there are two actuators at each end of the domain. This situation…
Motivated by engineering applications of subsea installation by deepwater construction vessels in oil drilling, and of aid delivery by unmanned aerial vehicles in disaster relief, we develop output-feedback boundary control of…
We develop a non-collocated, observer-based output-feedback law for a class of continua of linear hyperbolic PDE systems, which are viewed as the continuum version of $n+m$, general heterodirectional hyperbolic systems as $n\to\infty$. The…
This paper presents a model-based, adaptive, nonlinear controller for the bicopter stabilization and trajectory-tracking problem. The nonlinear controller is designed using the backstepping technique. Due to the non-invertibility of the…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
To stabilize PDE models, control laws require space-dependent functional gains mapped by nonlinear operators from the PDE functional coefficients. When a PDE is nonlinear and its "pseudo-coefficient" functions are state-dependent, a…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
This paper presents a safe output regulation control strategy for a class of systems modeled by a coupled $2\times 2$ hyperbolic PDE-ODE structure, subject to fully distributed disturbances throughout the system. A state-feedback controller…
We consider nonlinear control systems for which there exist some structural obstacles to the design of classical continuous stabilizing feedback laws. More precisely, it is studied systems for which the backstepping tool for the design of…
This paper considers a collection of networked nonlinear dynamical systems, and addresses the synthesis of feedback controllers that seek optimal operating points corresponding to the solution of network-wide constrained optimization…
This paper considers the backstepping state feedback control of coupled linear parabolic PDEs with spatially varying coefficients and bilateral actuation. By making use of the folding technique, a system representation with unilateral…
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…
This paper presents a boundary control scheme for prescribed-time (PT) stable of flexible string systems via backstepping method, and the dynamics of such systems modeled by Hamilton's principle is described as second-order hyperbolic…