Related papers: Output feedback stabilization for heat equations w…
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback…
This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction-diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the…
This paper investigates a minimal time control problem for the heat equation with multiple impulse controls. We first establish the maximum principles for this problem and then prove the equivalence between the minimal time impulse control…
The paper describes a novel method of sampled-data in space (spatial variable) control of scalar semilinear systems of parabolic and hyperbolic type with unknown parameters and distributed disturbances. A finite set of sampled-data in the…
In this paper, we analyze the output stabilization problem for cascaded nonlinear ODE with $1-d$ heat diffusion equation affected by both in-domain and boundary perturbations. We assume that the only available part of states is the first…
We study local stabilization of nonlinear control systems under explicit gain constraints on the feedback law. Using a quantitative refinement of Brockett's openness condition, we introduce the notion of a maximal continuous openness rate…
This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…
This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…
This paper studies the periodic feedback stabilization for a class of linear $T$-periodic evolution equations.Several equivalent conditions on the linear periodic feedback stabilization are obtained. These conditions are related with the…
We study scalar delay equations $$\dot{x} (t) = \lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\lambda, \, b$, and two positive time delays $1,\ p/2$. We assume supercritical…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
In this paper, we study time optimal control problems for heat equations on $\Omega\times \mathbb{R}^+$. Two properties under consideration are the existence and the bang-bang properties of time optimal controls. It is proved that those two…
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that…
Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals of tens of milliseconds. Low-power wireless technology is preferred for…
Proportional control can be realized directly through the amplification of analog signals, and it also has the advantage of easy tuning parameters in digital signal control. However, it is difficult for the proportional control to preset…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
Predictor-based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal…
It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by…
We investigate some structural properties of an efficient feedback law that stabilize linear time-reversible systems with an arbitrarily large decay rate. After giving a short proof of the generation of a group by the closed-loop operator,…
In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is…