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Leeuwen, Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization
 IEEE Transactions on Automatic Control
"... Abstract—In this paper, we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics. Models of uncertainties are allowed to be nonlinearly parameterized, and required to be smooth and monotonic functions of linear functionals of the para ..."
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Abstract—In this paper, we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics. Models of uncertainties are allowed to be nonlinearly parameterized, and required to be smooth and monotonic functions of linear functionals of the parameters. The mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded, reach a neighborhood of the target set, and the mismatches between the modeled uncertainties and their compensator converge to zero. With respect to parameter convergence, a standard persistent excitation condition suffices to ensure that it is exponential. When a weaker, nonlinear version of persistent excitation is satisfied, asymptotic convergence is guaranteed. The spectrum of possible applications ranges from tyreroad slip control to asynchronous message transmission in spiking neural oscillators. Index Terms—Adaptive control, exponential convergence, monotone functions, nonequilibrium dynamics, nonlinear parametrization, (nonlinear) persistent excitation, parameter estimation, unstable. I.
Invariant template matching in systems with spatiotemporal coding: a matter of instability. Neural Netw
, 2009
"... We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image ..."
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Cited by 5 (1 self)
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We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.
Parameter estimation of sigmoid superpositions: dynamical system approach
 Neural Comput
, 2003
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Natural Wave Control in Lattices of Linear Oscillators
, 2012
"... The problem of natural wave control involves steering a lattice of oscillators towards a desired natural (i.e. zeroinput) assignment of energy and phase across the lattice. This problem is formulated and solved for lattices of linear oscillators via a passivitybased approach. Numerical simulations ..."
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The problem of natural wave control involves steering a lattice of oscillators towards a desired natural (i.e. zeroinput) assignment of energy and phase across the lattice. This problem is formulated and solved for lattices of linear oscillators via a passivitybased approach. Numerical simulations of 1D and 2D linear lattices and a 1D lattice of nonlinear oscillators confirm the effectiveness of the proposed controls.
Convergence
, 2009
"... patterns. Matching is required to be tolerant to various combinations of image perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, and, as special cases, invariant transformation groups such as translation and rotations, as well as unmo ..."
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patterns. Matching is required to be tolerant to various combinations of image perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, and, as special cases, invariant transformation groups such as translation and rotations, as well as unmodeled uncertainties (noise). For a system to deal with such perturbations in an efficient way, they are to be handled through a minimal number of channels and by simple adaptation mechanisms. These normative requirements can be met within the mathematical framework of weakly attracting sets. We discuss explicit implementation of this principle in neural systems and show that it naturally explains a range of phenomena in biological vision, such as mental rotation, visual search, and the presence of multiple time scales in adaptation. We illustrate our results with an application to a realistic pattern recognition problem. © 2009 Elsevier Ltd. All rights reserved. 1. Notational preliminaries We define an image as a mapping S0(x, y) from a class of locally bounded mappings S ⊆ L∞(Ωx × Ωy), where Ωx ⊆ R, Ωy ⊆ R, and L∞(Ωx×Ωy) is the space of all functions f: Ωx×Ωy → R such
Proceedings of the American Control Confermce San Diego, California l June 1999 Swinging Up of Nonaffine in Control Pendulum
"... stable equilibrium point stabilization The problems of global stabilization of any prescribed energy level of the pendulum and the upright unstable equilibrium point of the pendulum are solved. The proposed stabilizing algorithm for the upright equilibrium position is based on a VSSlike modificat ..."
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stable equilibrium point stabilization The problems of global stabilization of any prescribed energy level of the pendulum and the upright unstable equilibrium point of the pendulum are solved. The proposed stabilizing algorithm for the upright equilibrium position is based on a VSSlike modification of the energyspeedgradient method. The qualitative description of the transient behaviour of the closed loop system is obtained. 1
CONTROL OF TWO PENDULUMSWITH ENERGY CONSTRAINTS
"... 1 A method for control of mechanical systems under phase constraints, applicable to energy control of Hamiltonian systems is proposed. The constrained energy control problem for two pendulums by a single control action is studied both analytically and numerically. It is shown that for a proper ch ..."
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1 A method for control of mechanical systems under phase constraints, applicable to energy control of Hamiltonian systems is proposed. The constrained energy control problem for two pendulums by a single control action is studied both analytically and numerically. It is shown that for a proper choice of penalty parameter of the algorithm any energy level for the one pendulum under any specified constraint on the energy of the other pendulum can be achieved. Simulation results confirm fast convergence rate of the algorithm. 1
Control of mechanical systems with constraints: two pendulums case study?
"... Abstract: A method for control of mechanical systems under phase constraints, applicable to energy control of Hamiltonian systems is proposed. The constrained energy control problem for two pendulums by a single control action is studied both analytically and numerically. It is shown that for a prop ..."
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Abstract: A method for control of mechanical systems under phase constraints, applicable to energy control of Hamiltonian systems is proposed. The constrained energy control problem for two pendulums by a single control action is studied both analytically and numerically. It is shown that for a proper choice of penalty parameter of the algorithm any energy level for the one pendulum under any specified constraint on the energy of the other pendulum can be achieved. Simulation results confirm fast convergence rate of the algorithm. 1.