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94
Stable Adaptive Control and Recursive Identification Using Radial Gaussian Networks
 Proc. IEEE Conf. Decis. Control
, 1991
"... Previous work has provided the theoretical foundations of a constructive design procedure for uniform approximation of smooth functions to a chosen degree of accuracy using networks of gaussian radial basis functions. This construction and the guaranteed uniform bounds were then shown to provide the ..."
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Previous work has provided the theoretical foundations of a constructive design procedure for uniform approximation of smooth functions to a chosen degree of accuracy using networks of gaussian radial basis functions. This construction and the guaranteed uniform bounds were then shown to provide the basis for stable adaptive neurocontrol algorithms for a class of nonlinear plants. This paper details and extends these ideas in three directions: first some practical details of the construction are provided, explicitly illustrating the relation between the free parameters in the network design and the degree of approximation error on a particular set. Next, the original adaptive control algorithm is modified to permit incorporation of additional prior knowledge of the system dynamics, allowing the neurocontroller to operate in parallel with conventional fixed or adaptive controllers. Finally, it is shown how the gaussian network construction may also be utilized in recursive identificatio...
From Theory to Practice: Distributed Coverage Control Experiments with Groups of Robots
"... Summary. A distributed algorithm is presented that causes a network of robots to spread out over an environment, while aggregating in areas of high sensory interest. The algorithm is a discretetime interpretation of a controller previously introduced by the authors. The algorithmic implications of ..."
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Summary. A distributed algorithm is presented that causes a network of robots to spread out over an environment, while aggregating in areas of high sensory interest. The algorithm is a discretetime interpretation of a controller previously introduced by the authors. The algorithmic implications of implementing this controller on a physical platform are discussed, and results are presented for 16 robots in two experiments. It is found that the algorithm performs well despite the presence of realworld complications. 1
A Synthesis Of Reinforcement Learning And Robust Control Theory
, 2000
"... OF DISSERTATION A SYNTHESIS OF REINFORCEMENT LEARNING AND ROBUST CONTROL THEORY The pursuit of control algorithms with improved performance drives the entire control research community as well as large parts of the mathematics, engineering, and artificial intelligence research communities. A funda ..."
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OF DISSERTATION A SYNTHESIS OF REINFORCEMENT LEARNING AND ROBUST CONTROL THEORY The pursuit of control algorithms with improved performance drives the entire control research community as well as large parts of the mathematics, engineering, and artificial intelligence research communities. A fundamental limitation on achieving control performance is the conflicting requirement of maintaining system stability. In general, the more aggressive is the controller, the better the control performance but also the closer to system instability.
Convergence rates of Approximation by Translates
 AI Memo 1288 (AI Laboratory, MIT
, 1995
"... In this paper we consider the problem of approximating a function belonging to some function space \Phi by a linear combination of n translates of a given function G. ..."
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In this paper we consider the problem of approximating a function belonging to some function space \Phi by a linear combination of n translates of a given function G.
Optimal Control by Least Squares Support Vector Machines
 Neural Networks
, 2001
"... Support vector machines have been very successful in pattern recognition and function estimation problems. In this paper we introduce the use of least squares support vector machines (LSSVM's) for the optimal control of nonlinear systems. Linear and neural full static state feedback controllers are ..."
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Cited by 9 (3 self)
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Support vector machines have been very successful in pattern recognition and function estimation problems. In this paper we introduce the use of least squares support vector machines (LSSVM's) for the optimal control of nonlinear systems. Linear and neural full static state feedback controllers are considered. The problem is formulated in such a way that it incorporates the Nstage optimal control problem as well as a least squares support vector machine approach for mapping the state space into the action space. The solution is characterized by a set of nonlinear equations. An alternative formulation as a constrained nonlinear optimization problem in less unknowns is given, together with a method for imposing local stability in the LSSVM control scheme. The results are discussed for support vector machines with radial basis function kernel. Advantages of LSSVM control are that no number of hidden units has to be determined for the controller and that no centers have to be specied for the Gaussian kernels when applying Mercer's condition. The curse of dimensionality is avoided in comparison with dening a regular grid for the centers in classical radial basis function networks. This is at the expense of taking the trajectory of state variables as additional unknowns in the optimization problem, while classical neural network approaches typically lead to parametric optimization problems. In the SVM methodology the number of unknowns equals the number of training data, while in the primal space the number of unknowns can be innite dimensional. The method is illustrated both on stabilization and tracking problems including examples on swinging up an inverted pendulum with local stabilization at the endpoint and a tracking problem for a ball and beam system. Keywords. N...
Stable MultiInput MultiOutput Adaptive Fuzzy/Neural Control
, 1999
"... In this letter, stable direct and indirect adaptive controllers are presented that use Takagi–Sugeno (T–S) fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multiinput multioutput (MI ..."
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In this letter, stable direct and indirect adaptive controllers are presented that use Takagi–Sugeno (T–S) fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multiinput multioutput (MIMO) square nonlinear plants with poorly understood dynamics. The direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics, while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics. We prove that with or without such knowledge the adaptive schemes can “learn” how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of the reference inputs. We do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero.
Nonlinear Iterative Learning by an Adaptive Lyapunov Technique
, 1999
"... We consider the iterative learning control problem from an adaptive control viewpoint. It is shown that many standard adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ILC problem. In particular we show that many of the common assum ..."
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We consider the iterative learning control problem from an adaptive control viewpoint. It is shown that many standard adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ILC problem. In particular we show that many of the common assumptions of nonlinear iterative learning control can be relaxed: eg. we relax the common linear growth asssumption on the nonlinearities and handle systems of arbitrary relative degree. Furthermore it is shown that these new ILC designs have the power to solve a new ILC problem: the learning of unseen trajectories (generalisation) . It is shown that generally a linear rate of convergence of the MSE can be achieved, and some simple robustness analyses are given. For linear plants we show that a linear rate of MSE convergence can be achieved for nonminimum phase plants. 1 Introduction The purpose of this paper is to consider the Iterative Learning Control (ILC) problem from an adaptive control...
Learning composite adaptive control for a class of nonlinear systems
 In IEEE International Conference on Robotics and Automation
, 2004
"... Abstract — In our recent work, an adaptive composite control technique was suggested for nonlinear adaptive control with statistical learning methods. While this original work was restricted to a simple class of nonlinear SISO systems that were linear in the inputs, in this paper we present a more g ..."
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Cited by 8 (4 self)
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Abstract — In our recent work, an adaptive composite control technique was suggested for nonlinear adaptive control with statistical learning methods. While this original work was restricted to a simple class of nonlinear SISO systems that were linear in the inputs, in this paper we present a more general treatment of learning a composite controller for the class of nonlinear systems characterized by the form ˙x = f(x)+g(x)u. We will first examine such systems in the first order SISO framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Second, we generalize our adaptive controller to higher order SISO systems, and discuss the application to MIMO problems. We evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control. I.
The fusion of computationally intelligent methodologies and slidingmode control—a survey
 IEEE Transactions on Industrial Electronics
, 2001
"... Abstract—This paper surveys how some “intelligence ” can be incorporated in slidingmode controllers (SMCs) by the use of computational intelligence methodologies in order to alleviate the wellknown problems met in practical implementations of SMCs. The use of variablestructure system theory in des ..."
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Abstract—This paper surveys how some “intelligence ” can be incorporated in slidingmode controllers (SMCs) by the use of computational intelligence methodologies in order to alleviate the wellknown problems met in practical implementations of SMCs. The use of variablestructure system theory in design and stability analysis of fuzzy controllers is also discussed by drawing parallels between fuzzy control and SMCs. An overview of the research and applications reported in the literature in this respect is presented. Index Terms—Computational intelligence, slidingmode control, soft computing.
Consensus learning for distributed coverage control
 in Proc. of ICRA
, 2008
"... Abstract — A decentralized controller is presented that causes a network of robots to converge to a near optimal sensing configuration, while simultaneously learning the distribution of sensory information in the environment. A consensus (or flocking) term is introduced in the learning law to allow ..."
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Abstract — A decentralized controller is presented that causes a network of robots to converge to a near optimal sensing configuration, while simultaneously learning the distribution of sensory information in the environment. A consensus (or flocking) term is introduced in the learning law to allow sharing of parameters among neighbors, greatly increasing learning convergence rates. Convergence and consensus is proven using a Lyapunovtype proof. The controller with parameter consensus is shown to perform better than the basic controller in numerical simulations. I.