Control For Nonlinear Large-scale Systems Research Articles

Special issue on robust stability and control of large-scale nonlinear systems

In a broad sense, large-scale systems theory is concerned with the analysis and design of often very high-dimensional systems that admit some kind of partition into smaller subsystems. Research in linear large-scale systems analysis and synthesis can be traced back to at least the 1970s. Recently, interest in this subject has been revived by new developments in nonlinear systems and control, which include but are not limited to dissipative systems theory, input-to-state stability, and various Lyapunov and smallgain design schemes. Systems and control theory itself has seen many important advances since the 1970s, including, e.g., concepts like control Lyapunov functions, effective implementations of nonlinear model predictive control, or entire emerging areas like hybrid systems and cooperative multi-agent systems. Naturally, these developments also leap into the area of large-scale systems. It is hence to be expected that the interest in this area will continue to increase, ultimately also due to, e.g., current research efforts in distributed model predictive control, next generation smart electricity grids, incorporating green and renewable energy sources, or bioand neuro-engineering. Many questions are associated with the theory of large-scale systems. A quite central one is about sufficient conditions on interconnections of a number of stable systems such that the composite system is also stable. Another one is how individual

Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer

An adaptive fuzzy decentralized backstepping output-feedback control approach is proposed for a class of nonlinear large-scale systems with completely unknown functions, the interconnections mismatched in control inputs, and without the measurements of the states. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and an adaptive high-gain observer is developed to estimate the unmeasured states. Using the designed high-gain observer, and combining the fuzzy adaptive control theory with backstepping approach, an adaptive fuzzy decentralized backstepping output-feedback control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer errors and the tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Finally, a simulation example is provided to show the effectiveness of the proposed approach.

Decentralized output-feedback control of large-scale nonlinear systems with sensor noise

AbstractThis paper studies decentralized output-feedback control of large-scale nonlinear systems in the presence of sensor noise. The measurement errors are dealt with by set-valued maps in the recursive control design of the subsystems. With appropriately designed decentralized controllers, the subsystems are rendered input-to-state stable (ISS) with respect to the outputs of the other subsystems and the disturbances. The robust stability of the closed-loop decentralized system is guaranteed by a recently developed cyclic-small-gain theorem.

Decentralised ℒ 1 adaptive control for large-scale non-linear systems with interconnected unmodelled dynamics

In this study, the authors investigate a decentralised ℒ1 adaptive controller design for a class of large-scale non-linear systems, with stable linear part and with interconnected non-linearities and unmodelled dynamics. The decentralised adaptive identifiers are presented to design the decentralised ℒ1 adaptive control scheme. The local ℒ1 adaptive controller for each subsystem ensures uniformly bounded transient tracking for subsystem's input and output, simultaneously. The controlled closed-loop decentralised adaptive system can recover the performance of the closed-loop large-scale centralised reference system by increasing the adaptation rates of local controllers. Simulation results for two inverted pendulums on carts are presented to show the effectiveness of the proposed control scheme.

Adaptive Fuzzy Decentralized Control for Large-Scale Nonlinear Systems With Time-Varying Delays and Unknown High-Frequency Gain Sign

In this paper, an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large-scale strict-feedback nonlinear systems without the measurements of the states. The nonlinear systems in this paper are assumed to possess unstructured uncertainties, time-varying delays, 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 special Nussbaum gain function is introduced to solve the problem of unknown high-frequency gain sign. Combining the backstepping technique with adaptive fuzzy control theory, an adaptive fuzzy decentralized robust output feedback control scheme is developed. In order to obtain the stability of the closed-loop system, a new lemma is given and proved. Based on this lemma and Lyapunov-Krasovskii functions, it is proved that all the signals in the closed-loop system are uniformly ultimately bounded and that the tracking errors can converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated from simulation results.

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances. The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms. Based on the internal model principle, a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances. According to the sensitivity approach, the optimal tracking control law for the ith nonlinear subsystem can be obtained. The optimal tracking control law for the nonlinear large-scale systems can be obtained. A numerical simulation shows that the method is effective.

Novel interaction prediction approach to hierarchical control of large-scale systems

In this paper, a new interaction prediction approach for hierarchical control of non-linear large-scale systems is presented. The proposed approach uses a new gradient-type coordination scheme which is robust with respect to the parameters' variation, and also has a good convergence rate. In classical coordination strategies, which can be divided into the gradient-type and substitution-type approaches, it is not possible to improve the robustness and the convergence rate at the same time, since by increasing one the other decreases. The proposed approach has the main advantages of the gradient-type algorithms in being independent of the parameter's variation and also the initial guess of the coordination vector. In addition, because of the proposed coordination strategy, in which the update of the coordination vector directly causes the reduction of the coordination error, the number of iterations is considerably reduced. The robustness and convergence rate of the proposed approach against the other interaction prediction approaches are shown through simulations of a benchmark problem. The simulation results also show the effectiveness of the proposed approach in solving constrained optimisation problems having non-quadratic cost functions. Comparisons are also made with the solutions obtained using centralised approach.

Optimization of large-scale systems using gradient-type interaction prediction approach

In this paper, a new decomposition–coordination framework is presented for two-level optimal control of large-scale nonlinear systems. In the proposed approach, decomposition is performed by defining an interaction vector, while coordination is based on a new interaction prediction approach. In the first level, sub-problems are solved for nonlinear dynamics using a gradient method, while in the second level, the coordination is done using the gradient of coordination errors. This is in contrast to the conventional gradient-type coordination schemes, where they use the gradient of Lagrangian function. It is shown that the proposed decomposition–coordination framework considerably reduces the number of iterations. Moreover, compared to the substitution-type coordination approaches which are well known for their fast convergence rates and limited convergence regions, the proposed approach is robust with respect to parameters’ variation in addition to its good convergence rate. The robustness and the convergence rate of the proposed approach in compare to the costate prediction method are shown through simulations of a benchmark problem. The results are also compared to the ones obtained using centralized approach.

Large Scale Nonlinear Control System Fine-Tuning Through Learning

Despite the continuous advances in the fields of intelligent control and computing, the design and deployment of efficient large scale nonlinear control systems (LNCSs) requires a tedious fine-tuning of the LNCS parameters before and during the actual system operation. In the majority of LNCSs the fine-tuning process is performed by experienced personnel based on field observations via experimentation with different combinations of controller parameters, without the use of a systematic approach. The existing adaptive/neural/fuzzy control methodologies cannot be used towards the development of a systematic, automated fine-tuning procedure for general LNCS due to the strict assumptions they impose on the controlled system dynamics; on the other hand, adaptive optimization methodologies fail to guarantee an efficient and safe performance during the fine-tuning process, mainly due to the fact that these methodologies involve the use of random perturbations. In this paper, we introduce and analyze, both by means of mathematical arguments and simulation experiments, a new learning/adaptive algorithm that can provide with convergent, an efficient and safe fine-tuning of general LNCS. The proposed algorithm consists of a combination of two different algorithms proposed by Kosmatopoulos (2007 and 2008) and the incremental-extreme learning machine neural networks (I-ELM-NNs). Among the nice properties of the proposed algorithm is that it significantly outperforms the algorithms proposed by Kosmatopoulos as well as other existing adaptive optimization algorithms. Moreover, contrary to the algorithms proposed by Kosmatopoulos , the proposed algorithm can operate efficiently in the case where the exogenous system inputs (e.g., disturbances, commands, demand, etc.) are unbounded signals.

Adaptive Fine-Tuning of Nonlinear Control Systems With Application to the Urban Traffic Control Strategy TUC

Practical large-scale nonlinear control systems require an intensive and time-consuming effort for the fine-tuning of their control parameters in order to achieve a satisfactory performance. In most cases, the fine-tuning process may take years and is performed by experienced personnel. The purpose of this paper is to introduce and analyze a systematic approach for the automatic fine-tuning of the control parameters of practical large-scale nonlinear control systems and investigate its efficiency when applied to the recently developed urban traffic control strategy traffic-responsive urban control. The proposed approach is based on a concept similar to the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The difference between the SPSA algorithm and the proposed approach is that, SPSA employs an approximation of the gradient of an appropriate objective function using only the most recent fine-tuning experiments, while in the proposed approach the approximation of the gradient is performed by using a linear-in-the-parameters approximator that incorporates information of a user-specified time-window of the past experiments. Mathematical analysis of the proposed approach establishes its convergence properties and that SPSA can be regarded as a special case of the proposed approach. Simulation results using the traffic network of the city of Chania, Greece-a typical urban traffic network containing all possible varieties of complex junction staging-demonstrate the efficiency of the proposed approach.

On the suboptimal solution for large scale non-linear control systems using neural networks

This work is aimed at looking into the determination of optimal control strategies of large scale non-linear systems. The basic idea consists of the decomposition of the global system into interconnected subsystems. We consider non-linear systems whose subsystems are linear with respect to their state and control; in other words, non-linearities are located in the interconnection terms. Then, for each subsystem, local optimal feedback gains are easily expressed in terms of interconnection vectors. Such optimisation has been successfully achieved using a neural net yielding the optimal gain at each step time. Some numerical examples are considered in order to illustrate the proposed approach.

Decentralised adaptive control for large-scale non-linear systems with unknown high-frequency-gain signs

For the first time, a decentralised adaptive control scheme for large-scale non-linear systems is proposed, which does not require a priori knowledge of subsystems' high-frequency-gain signs. In each local adaptive controller, a Nussbaum-type function is incorporated, and its argument is tuned online via an appropriately designed update law. The stability of the closed-loop system is analysed. It is shown that all signals in the closed-loop system are bounded, and that asymptotic regulation is achieved.

Decentralized Output Feedback Sliding Mode Control of Nonlinear Large-Scale Systems with Uncertainties

In this paper, a class of nonlinear large-scale interconnected systems with mismatched uncertainties is considered. Based on sliding mode control ideas, a kind of decentralized robust control scheme using only output information is presented to stabilize the system. The approach allows more general uncertain interconnections than all of the associated existing work and better robustness is achieved. Compared with existing decentralized output feedback schemes, it is unnecessary to solve Lyapunov equations and the so-called strict structural condition is avoided. Also, it is not necessary that the nominal subsystem is output feedback stabilizable. Finally, a simulation example is presented to illustrate the effectiveness of the results.

Decentralized robust control for nonlinear large-scale systems with similarity

In this paper, robust control for a class of nonlinear large-scale systems possessing similar subsystems is considered. The unmatched uncertainties considered may appear not only in the isolated subsystems but also in the interconnections. The only information required on the uncertainties is their bounding functions. By exploiting the similar structure of the large-scale system, two kinds of discontinuous nonlinear decentralized holographic-structure controllers (DHSCs), which are easily designed compared with general nonlinear controllers, are proposed to asymptotically stabilize the system. It is shown that the analysis and synthesis for nonlinear large-scale systems may be simplified using the similar structure. Finally, a numerical example is given to illustrate the methodology.

Decentralized adaptive fuzzy control for large-scale nonlinear systems

A decentralized adaptive fuzzy control scheme for a class of large-scale nonlinear systems is proposed in this paper. The design is based on the principle of sliding mode control and the approximation capability of fuzzy systems. The control architecture employs decentralized fuzzy systems to adaptively compensate for plant uncertainties. By using the Lyapunov function method, the control algorithm is proved to be globally stable, with tracking errors converging to a neighborhood of zero.

A decentralized approach to integrated flight control synthesis

A new approach to decoupled control of large-scale non-linear systems is applied to a dynamic flight control. Control synthesis is performed in two steps. First the nominal, programmed control is synthesized using the complete model of flight dynamics. This nominal control should realize the nominal trajectory under ideal conditions with no perturbations. In the second step the tracking of the nominal trajectory is realized. The system is viewed as a set of decoupled subsystems and for each subsystem local control is synthesized. Then, the stability of the overall system is analyzed and the global control is introduced to compensate coupling among some of the subsystems. A particular choice of subsystems in a case of flight control and of local and global control synthesis is proposed. A simulation of flight control with the proposed control law is also presented.

Optimal control of large-scale non-linear systems with time-delay

A hierarchical scheme is proposed for the optimal control of large-scale non-linear systems with multiple state and control delays. A linear approximation of a nonlinear system is defined about the precomputed and stored nominal trajectories. The system is then decomposed into N subsystems such that the delay terms and interaction terms can be treated as an extra input, named perturbation, to the linear non-delay subsystems. The scheme generates a partly closed-loop and partly open-loop control. The convergence of the algorithm is established. An example with quadratic cost is simulated and solved by the proposed scheme using the constant nominal trajectories. The results of computer simulation of the two control problems presented in the examples are included.

One New Method of Dynamic Flight Control

A new approach to decoupled control of large-scale nonlinear systems is applied to a dynamic flight control. Control synthesis is performed in two steps. First the nominal, programmed control is synthesized using the complete model of flight dynamics. This nominal control should realize nominal trajectory in ideal conditions with no perturbations. At the second step the tracking of nominal trajectory should be realized. The system is viewed as a set of decoupled subsystems and for each sybsystem local control is synthesized. Then, the stability of the over-all system is analyzed and the global control is introduced to compensate coupling among subsystems. In the paper particular choice of subsystems is proposed in a case of flight control and local and global control synthesis is proposed. A simulation of flight control with the proposed control law is also presented.