Challenges in Optimal Control of Nonlinear PDE-Systems

The workshop focussed on various aspects of optimal control problems for systems of nonlinear partial differential equations. In particular, discussions around keynote presentations in the areas of optimal control of nonlinear/non-smooth systems, optimal control of systems involving nonlocal operators, shape and topology optimization, feedback control and stabilization, sparse control, and associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, also aspects of control of fluid structure interaction problems as well as problems arising in the optimal control of quantum systems were considered

Challenges in Optimization with Complex PDE-Systems (hybrid meeting)

The workshop concentrated on various aspects of optimization problems with systems of nonlinear partial differential equations (PDEs) or variational inequalities (VIs) as constraints. In particular, discussions around several keynote presentations in the areas of optimal control of nonlinear or non-smooth systems, optimization problems with functional and discrete or switching variables leading to mixed integer nonlinear PDE constrained optimization, shape and topology optimization, feedback control and stabilization, multi-criteria problems and multiple optimization problems with equilibrium constraints as well as versions of these problems under uncertainty or stochastic influences, and the respectively associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, aspects of optimal control of data-driven PDE constraints (e.g. related to machine learning) were addressed

Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

Time-varying feedback stabilization of nonholonomic car-like mobile robots

Many nonholonomic mechanical systems, such as car-like mobile robots, are controllable but cannot be stabilized to given positions and orientations by using smooth pure-state feedback control. However, as shown in [18], such systems may still be stabilized by using smooth time-varying feedbacks, i.e. feedbacks which explicitly depend on the time-variable. This possibility is here applied to the stabilization of a class of nonlinear systems whose equations encompass simple car models. A set of stabilizing smooth time-varying feedbacks is derived and simulation results are given

Practical feedback stabilization of nonlinear control systems and applications

An important and challenging research subject in the field of nonlinear control systems is the impact of input constraints on control performance, which is more realistic in practical problems but much more difficult in mathematical analysis, such as the concepts of controllability, stability, stabilization, domain of attraction, controlled invariance and so on, especially when unstable systems are involved;More precisely, we consider the nonlinear system of the form x = f(x) on a smooth manifold M⊂ Rd together with the family of control-affine systems \dot x=f(x)+[sigma]spi=1mui(t)gi(x) with constrained control range U⊂ Rm. Our specific interest in this dissertation is to introduce the practical feedback control approach which provides a strategy that drives the phase-space trajectory of the nonlinear system arbitrarily close to the unstable limit sets (e.g. fixed points, periodic orbits, etc.) of x = f(x) and stabilizes forever the system in a certain small set;A software based on this theory has been successfully developed by the present author and his colleague Dr. Gerhard Hackl and applied to several models, such as a tunnel diode circuit model, a bacterial respiration model, a chemical reactor model etc.. In particular, we illustrate the numerical simulation of the global feedback controllers and the feedback controlled invariant sets of these examples

Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given