Stability analysis and performance design of fuzzy-model and neural-network-based control systems
Fuzzy-model-based (FMB) control approach offers a systematic and effective way to control nonlinear plants. Based on the fuzzy model, a nonlinear plant can be represented as a fuzzy combination of some local linear sub-systems. Similarly, a fuzzy controller, which is a fuzzy combination of some local linear sub-controllers, is employed to close the feedback loop to form a FMB control system. System stability and performance are two essential issues to be considered to put the fuzzy controller into practice. The Lyapunov stability theory is employed to investigate the global stability of the FMB control systems. Linear-matrix-inequality (LMI)-based stability conditions are derived to guarantee the system stability and to help design of a stable FMB control system. Considering a scalar performance index employed to measure quantitatively the system performance, LMI-based performance conditions are derived subject to the minimisation of the performance index. The solution to the LMI-based stability and performance conditions can be solved numerically using some convex programming techniques. With the LMI-based stability and performance conditions, a stable and well-performed FMB control system can be accomplished.
Performance optimization and topology design of neural networks
Neural network has been proved to be a universal approximator. A 3-layer feed-forward neural network can approximate any nonlinear continuous function to an arbitrary accuracy in a compact domain. Neural networks are widely applied in areas such as prediction, system modelling and control. Owing to its particular structure, a neural network is very good in learning using some learning algorithms such as GA and back propagation. In general, the learning steps of a neural network are as follows. First, a network structure is defined with a fixed number of inputs, hidden nodes and outputs. Second, an algorithm is chosen to realise the learning process. However, a fixed structure may not provide the optimal performance within a given training period. A small network may not provide good performance owing to its limited information processing power. A large network, on the other hand, may have some of its connections redundant. Moreover, the implementation cost for a large network is high. To enhance the learning and generalisation abilities, variable-parameter neural network are considered. Under this topology, the connection weights and/or the transfer functions depend on the input data. Consequently, the variable-parameter neural network is able to cope with the changes of the network inputs in different operating sub-domains. As a result, it seems to have an individual neural network to handle the inputs of each sub-domain. This characteristic is good for handling problems with large input data set in a large spatial domain. To determine the optimal network structure, a variable-structure neural network, which includes a switch in each connection link, is proposed. The on-off status of the switches effectively determines the network structure. Learning algorithm such as genetic algorithm (GA) is employed to search for the optimal connection weights and network structure under the proposed network topologies.
Synchronisation of chaotic systems
Chaotic synchronisation has drawn the researchers’ attention for many years by its practical applications in many engineering systems such as secure communication applications. In general, the objective of the chaotic synchronisation is to drive the system states of a response chaotic system to follow those of a drive chaotic system. As chaotic system is very sensitive to the initial conditions and highly nonlinear in nature, it is a very challenging task to control the chaotic systems. To synchronise two chaotic systems, various control approaches can be found in the literature. In general, the main idea is to modify the chaotic dynamical behaviour of the response chaotic system with the use of appropriate control actions to realise synchronisation. In recent years, fuzzy control techniques have been widely applied to deal with the chaotic synchronisation problem. Based on the fuzzy-model-based approach, various chaotic systems are represented by the T-S fuzzy models. Fuzzy controller is then proposed to perform the synchronisation task. LMI-based stability conditions are derived to achieve the fuzzy controller to realise the chaotic synchronisation.
Genetic algorithm (GA) is a directed random search technique that is widely applied in optimisation problems. It is especially useful for complex optimisation problems when the number of parameters is large and the analytical solutions are difficult to obtain. GA can help find out the globally optimal solution over a domain. It has been applied in different areas such as fuzzy control, path planning, modelling and classification, tuning parameters of neural/neural-fuzzy networks and etc. Different selection schemes and genetic operators have been proposed. The GA process can be summarised as follows. First, a population of chromosomes is created. Second, the chromosomes are evaluated by a defined fitness function. Third, some of the chromosomes are selected for performing genetic operations. Fourth, the genetic operations of crossover and mutation are performed. The produced offspring replaces their parents in the population. This GA process repeats until a user-defined criterion is reached. To enhance the efficiency of GA in terms of learning ability and convergence rate, various selection processes and genetic operators are developed and investigated.
Dr H.K. Lam, Leader of the Haptics Lab