Distributed control of spatially invariant systems

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H₂ and H_∞, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed     

Isochronous sets of invariant control systems

Let G be a connected Lie group with Lie algebra g and Σ=(G,D) a controllable invariant control system. A subset A⊂G is said to be isochronous if there exists a uniform time T_A>0 such that any two arbitrary elements in A can be connected by a positive orbit of Σ at exact time T_A. In this paper, we search for classes of Lie groups G such that any Σ has the following property: there exists an increasing sequence of open neighborhoods (V_n)_n≥0 of the identity in G such that the group can be decomposed in isochronous rings W_n=V_n+1−V_n. We characterize this property in algebraic terms and we show that three classes of Lie groups satisfy this property: completely solvable simply connected Lie groups, semisimple Lie groups and reductive Lie groups.     

线性控制系统的无界多面体不变集

本文利用非光滑分析方法,讨论了线性控制系统的无界多面体不变集问题.当无界多面体的极方向满足一定条件时,得到了该无界多面体为一类线性控制系统弱不变集的判别方法.然后在更一般的线性控制系统下给出了无界多面体为强不变集的充分条件.最后给出两个应用实例.     

Modal control of linear time invariant systems

A procedure is presented for the determination of a linear control law (for a system with one input) such that the resultant closed–loop System has specified eigenvalues. The design procedure is simpler than existing techniques.     

Fuzzy sliding-mode control with rule adaptation for nonlinear systems

Abstract: A fuzzy sliding-mode control with rule adaptation design approach with decoupling method is proposed. It provides a simple way to achieve asymptotic stability by a decoupling method for a class of uncertain nonlinear systems. The adaptive fuzzy sliding-mode control system is composed of a fuzzy controller and a compensation controller. The fuzzy controller is the main rule regulation controller, which is used to approximate an ideal computational controller. The compensation controller is designed to compensate for the difference between the ideal computational controller and the adaptive fuzzy controller. Fuzzy regulation is used as an approximator to identify the uncertainty. The simulation results for two cart–pole systems and a ball–beam system are presented to demonstrate the effectiveness and robustness of the method. In addition, the experimental results for a tunnelling robot manipulator are given to demonstrate the effectiveness of the system.     

Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.     

On almost invariant subspaces of structural systems anddecentralized control

Graph-theoretic conditions are obtained for a structured system to have the property that the supremal L_p-almost invariant (controllability) subspace is generically the entire state space and that the infimal ^L_p-almost conditional invariant (complementary observability) subspace is generically the zero subspace. The conditions are used to determine stabilizability of structured interconnected systems by means of decentralized feedback control. Although the obtained graph-theoretic conditions are conservative, they are considered satisfactory to the extent that the benefits of easy testability involving only binary calculations outweigh the conservativeness in the results     

A new approach for simplification and control of linear time invariant systems

Microsystem Technologies - This study presents a new approach for system simplification and control. This approach is based on the behaviour of growth and reproduction of weed plants namely...     

On the computation of convex robust control invariant sets for nonlinear systems

In this paper we provide a method to compute robust control invariant sets for nonlinear discrete-time systems. A simple criterion to evaluate if a convex set in state space is a robust control invariant set for a nonlinear uncertain system is presented. The criterion is employed to design an algorithm for computing a polytopic robust control invariant set. The method is based on the properties of DC functions, i.e. functions which can be expressed as the difference of two convex functions. Since the elements of a wide class of nonlinear functions have DC representation or, at least, admit an arbitrarily close approximation, the method is quite general. The algorithm requires relatively low computational resources.     

Sliding mode control with uncertainty adaptation for uncertain input-delay systems

This paper deals with a sliding mode control with uncertainty adaptation for the robust stabilization of uncertain input delay systems. The types of uncertainties comprise unknown time-varying non-linear parameter perturbations and external disturbance. A sliding surface including a state predictor is employed to compensate for the input delay. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation scheme based on the sliding surface. Then, a robust control law with uncertainty adaptation is derived to ensure the existence of the sliding mode.     

Online adaptation of reference trajectories for the control of walking systems

A simple and widely used way to make a robotic system walk without falling is to make it track a reference trajectory in one way or another, but the stability obtained this way may be limited and even small perturbations may lead to a fall. We propose here a series of heuristics to improve the stability that can be obtained from such a tracking control law, through an online adaptation of the choice of the reference trajectory being tracked. Encouraging simulations are obtained in the end on a simple planar biped model.     

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H     

Terminal bang-bang impulsive control of linear time invariant dynamic systems

For a linear time-invariant dynamic system with bang-bang impulsive actuators whose position (off, on negative, or on positive) is determined by the switching points in time, an algorithm is developed that makes it possible to use methods of modal control for solving the terminal control problem. This algorithm is used to control the rendezvous of space vehicles with constant thrust engines arranged along the axes of a Cartesian reference frame.     

Constrained control of switching systems: a positive invariant approach

This paper presents conditions for the stabilization of switching discrete-time linear systems with constrained control by using a positive invariance approach. A state feedback control law is used to construct the stabilizing controller. A numerical example is presented to illustrate the technique.     

A decomposition approach to distributed control of spatially invariant systems

This note considers the decentralized control of spatially invariant systems, i.e., systems of homogeneous interacting components. The main idea is for individual components to model interactions with neighbors as disturbances that satisfy certain magnitude bounds while simultaneously self-imposing symmetric magnitude bounds. These magnitude bounds can be interpreted as negotiated levels of interaction among components. It turns out that this approach is equivalent to constructing a feedback that is robustly stabilizing with structured uncertainties.     

Identification in automatic control systems

There are many concepts of system identification, and in this paper a comparison is made between different approaches based primarily on experimental identification with respect to the criteria of optimality selected for achieving identification, the mathematical models considered, the computing techniques used, and the kind and form of the input signal selected. Linear, non-linear, dynamic, and noisy systems are considered as well as adaptive models and stochastic approximations. It is concluded that although significant progress in system identification has been made, many problems remain, and among them is the determination of modeling accuracy especially for non-linear, noisy systems.     

Hierarchical robust systems for magnetic plasma control in tokamaks with adaptation

We consider synthesis and modeling of hierarchical robust magnetic control systems for plasma in tokamaks with adaptation of the magnetic axis’ vertical position. The studies were done for ITER (Cadarache, France) and Globus-M (St. Petersburg, Russia) tokamaks. Our original synthesis method ensures an improvement in performance for the shape of the plasma by resolving the contradiction between position and plasma shape via adaptation in a hierarchical system. Numerical modeling of synthesized control systems on multivariable linear models of plasma and nonlinear plasma-physics code DINA that unites basic equations of plasma dynamics in a magnetic field has shown the efficiency of the proposed approach and a possibility to apply it in a physical experiment.