Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> Decentralized robust adaptive controller designs for large-scale interconnected systems are investigated. Motivated by real mechanical systems, the authors consider a general representation of interconnections when the strength of the interconnections is bounded by a pth-order polynomial in states. This is in contrast to other studies which have made simpler assumptions about the strength of the interconnections. The authors investigate several scenarios as the control computations become more distributed until the controllers are completely decentralized. The possible bound of the interconnections is assumed to be known for the decentralized semiadaptive controller. Without the knowledge of these bounds, two adaptive controllers are designed: a decentralized adaptive controller with partially centralized compensation and a fully adaptive decentralized controller. > <s> BIB001 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> When the direct model reference adaptive control (MRAC) scheme with first-order local estimators is employed to design totally decentralized controllers, the stability result can only be applied to a system with all of its nominal subsystem relative degrees less than or equal to two. In this paper, this restriction is relaxed and it is achieved by employing the parameter projection together with static normalization. To implement the local controllers, no a priori knowledge of the subsystem unmodeled dynamics and no information exchange between subsystems are required. Global stability is established for the closed-loop system and small in the mean tracking error is ensured. With this analysis, the class of interactions and subsystem unmodeled dynamics can be enlarged to include those having infinite memory. <s> BIB002 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> Presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large-scale systems using nonlinear output feedback. The proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities. Any decentralized system in the family may have an unknown, nonzero equilibrium point. Partially decentralized reduced-order filters are presented to recover the unmeasured states. The recursive, decentralized, output-feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements. The effectiveness of the decentralized algorithm is supported by simulation results. <s> BIB003 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> In this paper, D-type iterative learning control schemes, which guarantee that the desired output is tracked precisely through iteration, are presented. Both off-line and on-line schemes are considered for a class of nonlinear systems. In both schemes, the learning gain may be time-varying and thus possesses larger scope for adjustment. Specifically, not only the input but also the initial state is iterated in the algorithms, and the output channel is fully nonlinear. Then, sufficient conditions are presented which guarantee the convergence of the proposed algorithms. The desired input and desired state are not assumed to be known a priori. Finally, the results are applied to a robotic system through simulation, which demonstrates the effectiveness of the method. <s> BIB004 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> The problem of decentralized stabilization is considered for a class of large-scale time-varying systems with delayed state perturbations in the interconnections. In this note, the upper bounds of the uncertainties in the interconnections are assumed to be unknown. The adaptation laws are proposed to estimate such unknown bounds, and by making use of their updated values, a class of decentralized memoryless state feedback controllers is constructed. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the solutions to the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly ultimately bounded. Finally, a numerical example is given to demonstrate the validity of the results. <s> BIB005 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> In this note, the problem of decentralized model reference adaptive variable structure control for a class of perturbed large-scale systems with varying time-delay interconnections is investigated. Based on the Lyapunov stability theorem, an adaptive variable structure control strategy for solving the robust tracking problem without the knowledge of upper bound of perturbations is developed. The use of adaptive technique is to adapt the unknown upper bound of perturbations so that the objective of globally asymptotical stability is achieved. Once the system enters the sliding manifold, the dynamics of controlled systems are insensitive to matching perturbations. Finally, an example is given to demonstrate the feasibility of the proposed control scheme. <s> BIB006 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> The problem of robust stabilization for a class of time-varying nonlinear large-scale systems subject to multiple time-varying delays in the interconnections is considered. The interconnections satisfy the match condition, and are bounded by nonlinear functions that may contain a high-order polynomial with a time delay. Without the knowledge of these bounds, we present adaptive state feedback controllers that are continuous and independent of time delays. Based on the Lyapunov stability theorem, we prove that the controllers can render the closed loop systems uniformly ultimately bounded stable. We also apply the result to constructing adaptive feedback controllers to stabilize a class of interconnected systems whose nominal systems are linear. Finally, several examples are given to show the potential of the proposed techniques. <s> BIB007 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> This paper considers the problem of robust decentralized adaptive output feedback stabilization for a class of interconnected systems with dynamic input and output interactions and nonlinear interactions by using MT-filters and the backstepping design method. It is shown that the closed-loop decentralized system based on MT-filters is globally uniformly bounded, all the signals except for the parameter estimates can be regulated to zero asymptotically, and the L"2 and L"~ norms of the system outputs are also be bounded by functions of design parameters. The scheme is demonstrated by a simulation example. <s> BIB008 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> In this paper, an adaptive fuzzy-decentralized robust output-feedback-control approach is proposed for a class of large-scale strict-feedback nonlinear systems with the unmeasured states. The large-scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties, unmodeled dynamics, and unknown high-frequency-gain sign. Fuzzy-logic systems are used to approximate the unstructured uncertainties, K-filters are designed to estimate the unmeasured states, and a dynamical signal and a special Nussbaum gain function are introduced into the control design to solve the problem of unknown high-frequency-gain sign and dominate unmodeled uncertainties, respectively. Based on the backstepping design and adaptive fuzzy-control methods, an adaptive fuzzy-decentralized robust output-feedback-control scheme is developed. It is proved that the proposed adaptive fuzzy-control approach can guarantee that all the signals in the closed-loop system are uniformly and ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by using simulation results. <s> BIB009 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> A novel neural network (NN)-based nonlinear decentralized adaptive controller is proposed for a class of large-scale, uncertain, interconnected nonlinear systems in strict-feedback form by using the dynamic surface control (DSC) principle, thus, the “explosion of complexity” problem which is observed in the conventional backstepping approach is relaxed in both state and output feedback control designs. The matching condition is not assumed when considering the interconnection terms. Then, NNs are utilized to approximate the uncertainties in both subsystem and interconnected terms. By using novel NN weight update laws with quadratic error terms as well as proposed control inputs, it is demonstrated using Lyapunov stability that the system states errors converge to zero asymptotically with both state and output feedback controllers, even in the presence of NN approximation errors in contrast with the uniform ultimate boundedness result, which is common in the literature with NN-based DSC and backstepping schemes. Simulation results show the effectiveness of the approach. <s> BIB010 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> This paper focuses on the problem of neural-network-based decentralized adaptive output-feedback control for a class of nonlinear strict-feedback large-scale stochastic systems. The dynamic surface control technique is used to avoid the explosion of computational complexity in the backstepping design process. A novel direct adaptive neural network approximation method is proposed to approximate the unknown and desired control input signals instead of the unknown nonlinear functions. It is shown that the designed controller can guarantee all the signals in the closed-loop system to be semiglobally uniformly ultimately bounded in a mean square. Simulation results are provided to demonstrate the effectiveness of the developed control design approach. <s> BIB011 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> A robust adaptive control design method was developed for uncertain Takagi-Sugeno fuzzy models with norm-bounded uncertainties. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel and the norm bound of the uncertainty is known, which is required in the traditional VSS-based fuzzy control design methods. We derive existence conditions of linear sliding surfaces guaranteeing the asymptotic stability in terms of constrained linear matrix inequalities (LMIs) and an LMI characterisation of such sliding surfaces is discussed. Also, an LMI-based algorithm is given to design the switching feedback control term and an adaptation law so that a stable sliding motion is induced in finite time. Finally, we give two examples to show the effectiveness of the proposed method. <s> BIB012 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analyse nonlinear systems. Therefore it is natural to treat adaptive control as a part of nonlinear control systems. Nonlinear and Adaptive Control Systems treats nonlinear control and adaptive control in a unified framework, presenting the major results at a moderate mathematical level, suitable for MSc students and engineers with undergraduate degrees. Topics covered include introduction to nonlinear systems; state space models; describing functions for common nonlinear components; stability theory; feedback linearization; adaptive control; nonlinear observer design; backstepping design; disturbance rejection and output regulation; and control applications, including harmonic estimation and rejection in power distribution systems, observer and control design for circadian rhythms, and discrete-time implementation of continuous-time nonlinear control laws. <s> BIB013 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> A modelling method is proposed and applied in fault detection for non-linear dynamic systems with bounded noises. Since the radial basis function (RBF) neural network is a universal approximator, it is used to model the non-linear system when the system runs without a fault. After some input and output data of the system are obtained, the centres of the hidden nodes are chosen using clustering technology. Assuming that the system noise and approximation error are unknown but bounded, the output weights of RBF neural network model of the system are determined by a linear-in-parameter set membership estimation algorithm. An interval containing the actual output of the system running without a fault can be easily predicted based on the result of the estimation. If the measured output is out of the predicted interval, it can be determined that a fault has occurred. Simulation results show the effectiveness of the proposed method. <s> BIB014 </s> Decentralised control for complex systems - an invited survey <s> Decentralised adaptive control <s> In this paper, using a neural-network-based online learning optimal control approach, a novel decentralized control strategy is developed to stabilize a class of continuous-time nonlinear interconnected large-scale systems. First, optimal controllers of the isolated subsystems are designed with cost functions reflecting the bounds of interconnections. Then, it is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control policies of the isolated subsystems. Next, an online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman equations related to the optimal control problem. Through constructing a set of critic neural networks, the cost functions can be obtained approximately, followed by the control policies. Furthermore, the dynamics of the estimation errors of the critic networks are verified to be uniformly and ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the present decentralized control scheme. <s> BIB015
Adaptive control was conceived in the 1950s. It has been most successful for plant models in which unknown/uncertain parameters appear linearly  . Unlike robust control, adaptive control BIB012 does not require priori information and knowledge for the bounds on these uncertain/unknown parameters. It is well-known that robust control guarantees that the system has desired performance if the uncertainties change within given bounds. In this case, the control law does not need to change. However, adaptive control is concerned with a control law that changes itself. The foundation of adaptive control is parameter estimation. The main idea of adaptive control is to maintain a desired system performance in the presence of uncertainties or unknown variation in plant parameters. When the parameters change, the system adapts to the changes in the system to maintain performance. Effectively, there is adaptation in the controller setting subject to the performance of the closed-loop system. How the controller parameters change is determined by the adaptive laws which are often designed based on the requirements for the designed adaptive control system BIB013 . When unknown parameters appear in large scale interconnected systems and the bounds on the uncertainties are not available, decentralised adaptive control is a good choice to maintain the system performance. A decentralised adaptive robust control scheme is proposed for a class of large-scale interconnected systems to guarantee the corresponding closed-loop systems ultimate boundedness in BIB005 , BIB007 and BIB008 . Interconnected systems with time delay are considered in BIB005 and BIB007 where it is required that the interconnections satisfy the matching condition. A decentralised adaptive output feedback controller to solve the asymptotic tracking problem was proposed in BIB003 where the matching condition is not required. Decentralised model reference adaptive control schemes are proposed in BIB002 and BIB006 which do not need information on the upper bound of the perturbations. The robust tracking problem is solved using model reference adaptive variable structure control but matching conditions are required for the local reference model in BIB006 . BIB001 proposed a decentralised adaptive controller to deal with a class of interconnected systems which are bounded by p th order polynomials in the states. Global stabilisation is considered in BIB002 where there is no restriction on the relative degree of the nominal subsystem. In this paper, parameter projection together with static normalisation is employed. In recent years, adaptive techniques have been successfully combined with intelligent control techniques such as fuzzy control BIB012 , neural networks BIB014 and learning control BIB004 ) to design decentralised controllers. Great attention has been paid to this area and many results have been achieved, for example, BIB009 , BIB011 , BIB010 and BIB015 . It is possible that correct limitations on the interconnections in decentralised adaptive control strategies may be overcome by the use of intelligent control concepts.