Active disturbance cancellation in nonlinear dynamical systems using neural networks

A proposal for the use of a time delay CMAC neural network for disturbance cancellation in nonlinear dynamical systems is presented. Appropriate modifications to the CMAC training algorithm are derived which allow convergent adaptation for a variety of secondary signal paths. Analytical bounds on the maximum learning gain are presented which guarantee convergence of the algorithm and provide insight into the necessary reduction in learning gain as a function of the system parameters. Effectiveness of the algorithm is evaluated through mathematical analysis, simulation studies, and experimental application of the technique on an acoustic duct laboratory model

Neural-Network-Based State Feedback Control of a Nonlinear Discrete-Time System in Nonstrict Feedback Form

In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability

Transition control based on grey, neural states

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Memristor models for machine learning

In the quest for alternatives to traditional CMOS, it is being suggested that digital computing efficiency and power can be improved by matching the precision to the application. Many applications do not need the high precision that is being used today. In particular, large gains in area- and power efficiency could be achieved by dedicated analog realizations of approximate computing engines. In this work, we explore the use of memristor networks for analog approximate computation, based on a machine learning framework called reservoir computing. Most experimental investigations on the dynamics of memristors focus on their nonvolatile behavior. Hence, the volatility that is present in the developed technologies is usually unwanted and it is not included in simulation models. In contrast, in reservoir computing, volatility is not only desirable but necessary. Therefore, in this work, we propose two different ways to incorporate it into memristor simulation models. The first is an extension of Strukov's model and the second is an equivalent Wiener model approximation. We analyze and compare the dynamical properties of these models and discuss their implications for the memory and the nonlinear processing capacity of memristor networks. Our results indicate that device variability, increasingly causing problems in traditional computer design, is an asset in the context of reservoir computing. We conclude that, although both models could lead to useful memristor based reservoir computing systems, their computational performance will differ. Therefore, experimental modeling research is required for the development of accurate volatile memristor models.Comment: 4 figures, no tables. Submitted to neural computatio

Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

Lyapunov based optimal control of a class of nonlinear systems

Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv

Automatic control of a multirotor

Objective of this thesis is to describe the design and realisation phases of a multirotor to be used for low risk and cost aerial observation. Starting point of this activity was a wide literature study related to the technological evolution of multirotors design and to the state of the art. Firstly the most common multirotor configurations were defined and, according to a size and performance based evaluation, the most suitable one was chosen. A detailed computer aided design model was drawn as basis for the realisation of two prototypes. The realised multirotors were “X-shaped” octorotors with eight coaxially coupled motors. The mathematical model of the multirotor dynamics was studied. “Proportional Integral Derivative” and “Linear Quadratic” algorithms were chosen as techniques to regulate the attitude dynamics of the multirotor. These methods were tested with a nonlinear model simulation developed in the Matlab Simulink environment. In the meanwhile the Arduino board was selected as the best compromise between costs and performance and the above mentioned algorithms were implemented using this platform thanks to its main characteristic of being completely “open source”. Indeed the multirotor was conceived to be a serviceable tool for the public utility and, at the same time, to be an accessible device for research and studies. The behaviour of the physical multirotor was evaluated with a test bench designed to isolate the rotation about one single body axis at a time. The data of the experimental tests were gathered in real time using a custom Matlab code and several indoor tests allowed the “fine tuning” of the controllers gains. Afterwards a portable “ground station” was conceived and realised in adherence with the real scenarios users needs. Several outdoor experimental flights were executed with successful results and the data gathered during the outdoor tests were used to evaluate some key performance indicators as the endurance and the maximum allowable payload mass. Then the fault tolerance of the control system was evaluated simulating and experimenting the loss of one motor; even in this critical condition the system exhibited an acceptable behaviour. The reached project readiness allowed to meet some potential users as the “Turin Fire Department” and to cooperate with them in a simulated emergency. During this event the multirotor was used to gather and transmit real time aerial images for an improved “situation awareness”. Finally the study was extended to more innovative control techniques like the neural networks based ones. Simulations results demonstrated their effectiveness; nevertheless the inherent complexity and the unreliability outside the training ranges could have a catastrophic impact on the airworthiness. This is a factor that cannot be neglected especially in the applications related to flying platforms. Summarising, this research work was addressed mainly to the operating procedures for implementing automatic control algorithms to real platforms. All the design aspects, from the preliminary multirotor configuration choice to the tests in possible real scenarios, were covered obtaining performances comparable with other commercial of-the-shelf platforms

Neural networks in control engineering

The purpose of this thesis is to investigate the viability of integrating neural networks into control structures. These networks are an attempt to create artificial intelligent systems with the ability to learn and remember. They mathematically model the biological structure of the brain and consist of a large number of simple interconnected processing units emulating brain cells. Due to the highly parallel and consequently computationally expensive nature of these networks, intensive research in this field has only become feasible due to the availability of powerful personal computers in recent years. Consequently, attempts at exploiting the attractive learning and nonlinear optimization characteristics of neural networks have been made in most fields of science and engineering, including process control. The control structures suggested in the literature for the inclusion of neural networks in control applications can be divided into four major classes. The first class includes approaches in which the network forms part of an adaptive mechanism which modulates the structure or parameters of the controller. In the second class the network forms part of the control loop and replaces the conventional control block, thus leading to a pure neural network control law. The third class consists of topologies in which neural networks are used to produce models of the system which are then utilized in the control structure, whilst the fourth category includes suggestions which are specific to the problem or system structure and not suitable for a generic neural network-based-approach to control problems. Although several of these approaches show promising results, only model based structures are evaluated in this thesis. This is due to the fact that many of the topologies in other classes require system estimation to produce the desired network output during training, whereas the training data for network models is obtained directly by sampling the system input(s) and output(s). Furthermore, many suggested structures lack the mathematical motivation to consider them for a general structure, whilst the neural network model topologies form natural extensions of their linear model based origins. Since it is impractical and often impossible to collect sufficient training data prior to implementing the neural network based control structure, the network models have to be suited to on-line training during operation. This limits the choice of network topologies for models to those that can be trained on a sample by sample basis (pattern learning) and furthermore are capable of learning even when the variation in training data is relatively slow as is the case for most controlled dynamic systems. A study of feedforward topologies (one of the main classes of networks) shows that the multilayer perceptron network with its backpropagation training is well suited to model nonlinear mappings but fails to learn and generalize when subjected to slow varying training data. This is due to the global input interpretation of this structure, in which any input affects all hidden nodes such that no effective partitioning of the input space can be achieved. This problem is overcome in a less flexible feedforward structure, known as regular Gaussian network. In this network, the response of each hidden node is limited to a -sphere around its center and these centers are fixed in a uniform distribution over the entire input space. Each input to such a network is therefore interpreted locally and only effects nodes with their centers in close proximity. A deficiency common to all feedforward networks, when considered as models for dynamic systems, is their inability to conserve previous outputs and states for future predictions. Since this absence of dynamic capability requires the user to identify the order of the system prior to training and is therefore not entirely self-learning, more advanced network topologies are investigated. The most versatile of these structures, known as a fully recurrent network, re-uses the previous state of each of its nodes for subsequent outputs. However, despite its superior modelling capability, the tests performed using the Williams and Zipser training algorithm show that such structures often fail to converge and require excessive computing power and time, when increased in size. Despite its rigid structure and lack of dynamic capability, the regular Gaussian network produces the most reliable and robust models and was therefore selected for the evaluations in this study. To overcome the network initialization problem, found when using a pure neural network model, a combination structure· _in which the network operates in parallel with a mathematical model is suggested. This approach allows the controller to be implemented without any prior network training and initially relies purely on the mathematical model, much like conventional approaches. The network portion is then trained during on-line operation in order to improve the model. Once trained, the enhanced model can be used to improve the system response, since model exactness plays an important role in the control action achievable with model based structures. The applicability of control structures based on neural network models is evaluated by comparing the performance of two network approaches to that of a linear structure, using a simulation of a nonlinear tank system. The first network controller is developed from the internal model control (IMC) structure, which includes a forward and inverse model of the system to be controlled. Both models can be replaced by a combination of mathematical and neural topologies, the network portion of which is trained on-line to compensate for the discrepancies between the linear model _ and nonlinear system. Since the network has no dynamic ·capacity, .former system outputs are used as inputs to the forward and inverse model. Due to this direct feedback, the trained structure can be tuned to perform within limits not achievable using a conventional linear system. As mentioned previously the IMC structure uses both forward and inverse models. Since the control law requires that these models are exact inverses, an iterative inversion algorithm has to be used to improve the values produced by the inverse combination model. Due to deadtimes and right-half-plane zeroes, many systems are furthermore not directly invertible. Whilst such unstable elements can be removed from mathematical models, the inverse network is trained directly from the forward model and can not be compensated. These problems could be overcome by a control structure for which only a forward model is required. The neural predictive controller (NPC) presents such a topology. Based on the optimal control philosophy, this structure uses a model to predict several future outputs. The errors between these and the desired output are then collected to form the cost function, which may also include other factors such as the magnitude of the change in input. The input value that optimally fulfils all the objectives used to formulate the cost function, can then be found by locating its minimum. Since the model in this structure includes a neural network, the optimization can not be formulated in a closed mathematical form and has to be performed using a numerical method. For the NPC topology, as for the neural network IMC structure, former system outputs are fed back to the model and again the trained network approach produces results not achievable with a linear model. Due to the single network approach, the NPC topology furthermore overcomes the limitations described for the neural network IMC structure and can be extended to include multivariable systems. This study shows that the nonlinear modelling capability of neural networks can be exploited to produce learning control structures with improved responses for nonlinear systems. Many of the difficulties described are due to the computational burden of these networks and associated algorithms. These are likely to become less significant due to the rapid development in computer technology and advances in neural network hardware. Although neural network based control structures are unlikely to replace the well understood linear topologies, which are adequate for the majority of applications, they might present a practical alternative where (due to nonlinearity or modelling errors) the conventional controller can not achieve the required control action