Issues on Stability of ADP Feedback Controllers for Dynamical Systems

This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called “adaptive critics” or “action-critic” networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in “model-free” development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse forms

Evolutionary design automation for control systems with practical constraints

The aim of this work is to explore the potential and to enhance the capability of evolutionary computation in the development of novel and advanced methodologies that enable control system structural optimisation and design automation for practical applications. Current design and optimisation methods adopted in control systems engineering are in essence based upon conventional numerical techniques that require derivative information of performance indices. These techniques lack robustness in solving practical engineering problems, which are often of a multi-dimensional, multi-modal nature. Using those techniques can often achieve neither global nor structural optimisation. In contrast, evolutionary mechanism learning tools have the ability to search in a multi-dimensional, multi-modal space, but they can not approach a local optimum as a conventional calculus-based method. The first objective of this research is to develop a reliable and effective evolutionary algorithm for engineering applications. In this thesis, a globally optimal evolutionary methodology and environment for control system structuring and design automation is developed, which requires no design indices to be differentiable. This is based on the development of a hybridised GA search engine, whose local tuning is tremendously enhanced by the incorporation of Hill-Climbing (HC), Simulated Annealing (SA) and Simplex techniques to improve the performance in search and design. A Lamarckian inheritance technique is also developed to improve crossover and mutation operations in GAs. Benchmark tests have shown that the enhanced hybrid GA is accurate, and reliable. Based on this search engine and optimisation core, a linear and nonlinear control system design automation suite is developed in a Java based platform-independent format, which can be readily available for design and design collaboration over corporate Intranets and the Internet. Since it has also made cost function unnecessary to be differentiable, hybridised indices combining time and frequency domain measurement and accommodating practical constraints can now be incorporated in the design. Such type of novel indices are proposed in the thesis and incorporated in the design suite. The Proportional plus Integral plus Derivative (PID) controller is very popular in real world control applications. The development of new PID tuning rules remains an area of active research. Many researchers, such as Åström and Hägglund, Ho, Zhuang and Atherton, have suggested many methods. However, their methods still suffer from poor load disturbance rejection, poor stability or shutting of the derivative control etc. In this thesis, Systematic and batch optimisation of PID controllers to meet practical requirements is achieved using the developed design automation suite. A novel cost function is designed to take disturbance rejection, stability in terms of gain and phase margins and other specifications into account in-the same time. Comparisons made with Ho's method confirm that the derivative action can play an important role to improve load disturbance rejection yet maintaining the same stability margins. Comparisons made with Åström’s method confirm that the results from this thesis are superior not only in load disturbance rejection but also in terms of stability margins. Further robustness issues are addressed by extending the PID structure to a free form transfer function. This is realised by achieving design automation. Quantitative Feedback Theory (QFTX, method offers a direct frequency-domain design technique for uncertain plants, which can deal non-conservatively with different types of uncertainty models and specifications. QFT design problems are often multi-modal and multi-dimensional, where loop shaping is .the most challenging part. Global solutions can hardly be obtained using analytical and convex or linear programming techniques. In addition, these types of conventional methods often impose unrealistic or unpractical assumptions and often lead to very conservative designs. In this thesis, GA-based automatic loop shaping for QFT controllers suggested by the Research Group is being furthered. A new index is developed for the design which can describe stability, load rejection and reduction of high frequency gains, which has not been achieved with existing methods. The corresponding prefilter can also be systematically designed if tracking is one of the specifications. The results from the evolutionary computing based design automation suite show that the evolutionary technique is much better than numerical methods and manual designs, i.e., 'high frequency gain' and controller order have been significantly reduced. Time domain simulations show that the designed QFT controller combined with the corresponding prefilter performs more satisfactorily

Optimal Control of Unknown Nonlinear System From Inputoutput Data

Optimal control designers usually require a plant model to design a controller. The problem is the controller\u27s performance heavily depends on the accuracy of the plant model. However, in many situations, it is very time-consuming to implement the system identification procedure and an accurate structure of a plant model is very difficult to obtain. On the other hand, neuro-fuzzy models with product inference engine, singleton fuzzifier, center average defuzzifier, and Gaussian membership functions can be easily trained by many well-established learning algorithms based on given input-output data pairs. Therefore, this kind of model is used in the current optimal controller design. Two approaches of designing optimal controllers of unknown nonlinear systems based on neuro-fuzzy models are presented in the thesis. The first approach first utilizes neuro-fuzzy models to approximate the unknown nonlinear systems, and then the feasible-direction algorithm is used to achieve the numerical solution of the Euler-Lagrange equations of the formulated optimal control problem. This algorithm uses the steepest descent to find the search direction and then apply a one-dimensional search routine to find the best step length. Finally several nonlinear optimal control problems are simulated and the results show that the performance of the proposed approach is quite similar to that of optimal control to the system represented by an explicit mathematical model. However, due to the limitation of the feasible-direction algorithm, this method cannot be applied to highly nonlinear and dimensional plants. Therefore, another approach that can overcome these drawbacks is proposed. This method utilizes Takagi-Sugeno (TS) fuzzy models to design the optimal controller. TS fuzzy models are first derived from the direct linearization of the neuro-fuzzy models, which is close to the local linearization of the nonlinear dynamic systems. The operating points are chosen so that the TS fuzzy model is a good approximation of the neuro-fuzzy model. Based on the TS fuzzy model, the optimal control is implemented for a nonlinear two-link flexible robot and a rigid asymmetric spacecraft, thus providing the possibility of implementing the well-established optimal control method on unknown nonlinear dynamic systems

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Control of large-scale structures with large uncertainties

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 279-300).Performance-based design is a design approach that satisfies motion constraints as its primary goal, and then verifies for strength. The approach is traditionally executed by appropriately sizing stiffnesses, but recently, passive energy dissipation systems have gained popularity. Semi-active and active energy dissipation systems have been shown to outperform purely passive systems, but they are not yet widely accepted in the construction and structural engineering fields. Several factors are impeding the application of semi-active and active damping systems, such as large modeling uncertainties that are inherent to large-scale structures, limited state measurements, lack of mechanically reliable control devices, large power requirements, and the need for robust controllers. In order to enhance acceptability of feedback control systems to civil structures, an integrated control strategy designed for large-scale structures with large parametric uncertainties is proposed. The control strategy comprises a novel controller, as well as a new semi-active mechanical damping device. Specifically, the controller is an adaptive black-box representation that creates and optimizes control laws sequentially during an excitation, with no prior training. The novel feature is its online organization of the input space. The representation only requires limited observations for constructing an efficient representation, which allows control of unknown systems with limited state measurements. The semi-active mechanical device consists of a friction device inspired by a vehicle drum brakes, with a viscous and a stiffness element installed in parallel. Its unique characteristic is its theoretical damping force reaching the order of 100 kN, using a friction mechanism powered with a single 12-volts battery. It is conceived using mechanically reliable technologies, which is a solution to large power requirement and mechanical robustness. The integrated control system is simulated on an existing structure located in Boston, MA, as a replacement to the existing viscous damping system. Simulation results show that the integrated control system can mitigate wind vibrations as well as the current damping strategy, utilizing only one third of devices. In addition, the system created effective control rules for several types of earthquake excitations with no prior training, performing similarly to an optimal controller using full parametric and state knowledge.by Simon Laflamme.Ph.D

Improving time efficiency of feedforward neural network learning

Feedforward neural networks have been widely studied and used in many applications in science and engineering. The training of this type of networks is mainly undertaken using the well-known backpropagation based learning algorithms. One major problem with this type of algorithms is the slow training convergence speed, which hinders their applications. In order to improve the training convergence speed of this type of algorithms, many researchers have developed different improvements and enhancements. However, the slow convergence problem has not been fully addressed. This thesis makes several contributions by proposing new backpropagation learning algorithms based on the terminal attractor concept to improve the existing backpropagation learning algorithms such as the gradient descent and Levenberg-Marquardt algorithms. These new algorithms enable fast convergence both at a distance from and in a close range of the ideal weights. In particular, a new fast convergence mechanism is proposed which is based on the fast terminal attractor concept. Comprehensive simulation studies are undertaken to demonstrate the effectiveness of the proposed backpropagataion algorithms with terminal attractors. Finally, three practical application cases of time series forecasting, character recognition and image interpolation are chosen to show the practicality and usefulness of the proposed learning algorithms with comprehensive comparative studies with existing algorithms