Results 1  10
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19
Complete search in continuous global optimization and constraint satisfaction, Acta Numerica 13
, 2004
"... A chapter for ..."
Approximate dynamic programming via iterated Bellman inequalities
, 2010
"... In this paper we introduce new methods for finding functions that lower bound the value function of a stochastic control problem, using an iterated form of the Bellman inequality. Our method is based on solving linear or semidefinite programs, and produces both a bound on the optimal objective, as w ..."
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In this paper we introduce new methods for finding functions that lower bound the value function of a stochastic control problem, using an iterated form of the Bellman inequality. Our method is based on solving linear or semidefinite programs, and produces both a bound on the optimal objective, as well as a suboptimal policy that appears to works very well. These results extend and improve bounds obtained by authors in a previous paper using a single Bellman inequality condition. We describe the methods in a general setting, and show how they can be applied in specific cases including the finite state case, constrained linear quadratic control, switched affine control, and multiperiod portfolio investment.
Providing a basin of attraction to a target region by computation of Lyapunovlike functions
 In IEEE Int. Conf. on Computational Cybernetics
, 2006
"... Abstract — In this paper, we present a method for computing a basin of attraction to a target region for nonlinear ordinary differential equations. This basin of attraction is ensured by a Lyapunovlike polynomial function that we compute using an interval based branchandrelax algorithm. This alg ..."
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Abstract — In this paper, we present a method for computing a basin of attraction to a target region for nonlinear ordinary differential equations. This basin of attraction is ensured by a Lyapunovlike polynomial function that we compute using an interval based branchandrelax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunovlike function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyperrectangles. Tests on an implementation are promising. I.
On parameterdependent Lyapunov functions for robust stability of linear systems
"... Abstract — For a linear system affected by real parametric uncertainty, this paper focuses on robust stability analysis via quadraticinthestate Lyapunov functions polynomially dependent on the parameters. The contribution is twofold. First, if n denotes the system order and m the number of parame ..."
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Cited by 2 (0 self)
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Abstract — For a linear system affected by real parametric uncertainty, this paper focuses on robust stability analysis via quadraticinthestate Lyapunov functions polynomially dependent on the parameters. The contribution is twofold. First, if n denotes the system order and m the number of parameters, it is shown that it is enough to seek a parameterdependent Lyapunov function of given degree 2nm in the parameters. Second, it is shown that robust stability can be assessed by globally minimizing a multivariate scalar polynomial related with this Lyapunov matrix. A hierarchy of LMI relaxations is proposed to solve this problem numerically, yielding simultaneously upper and lower bounds on the global minimum with guarantee of asymptotic convergence. I.
Finite alphabet control and estimation
 International Journal of Control, Automation and Systems
"... Abstract: In many practical problems in signal processing and control, the signal values are often restricted to belong to a finite number of levels. These questions are generally referred to as “finite alphabet ” problems. There are many applications of this class of problems including: onoff cont ..."
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Abstract: In many practical problems in signal processing and control, the signal values are often restricted to belong to a finite number of levels. These questions are generally referred to as “finite alphabet ” problems. There are many applications of this class of problems including: onoff control, optimal audio quantization, design of finite impulse response filters having quantized coefficients, equalization of digital communication channels subject to intersymbol interference, and control over networked communication channels. This paper will explain how this diverse class of problems can be formulated as optimization problems having finite alphabet constraints. Methods for solving these problems will be described and it will be shown that a semiclosed form solution exists. Special cases of the result include well known practical algorithms such as optimal noise shaping quantizers in audio signal processing and decision feedback equalizers in digital communication. Associated stability questions will also be addressed and several real world applications will be presented.
An alternative approach for nonlinear optimal control problems based on the method of moments
 Computational Optimization and Applications
"... We propose an alternative method for computing effectively the solution of nonlinear, fixedterminaltime, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The esse ..."
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We propose an alternative method for computing effectively the solution of nonlinear, fixedterminaltime, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a nonlinear, nonconvex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology. 1 1
1 A Dissipation Inequality for the Minimum Phase Property of Nonlinear Control Systems and Performance Limitations
"... Abstract — The minimum phase property is an important notion in systems and control theory. In this paper, a characterization of the minimum phase property of nonlinear control systems in terms of a dissipation inequality is derived. It is shown that this dissipation inequality is equivalent to the ..."
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Abstract — The minimum phase property is an important notion in systems and control theory. In this paper, a characterization of the minimum phase property of nonlinear control systems in terms of a dissipation inequality is derived. It is shown that this dissipation inequality is equivalent to the classical definition of the minimum phase property in the sense of Byrnes and Isidori, if the control system is affine in the input and the socalled inputoutput normal form exists. Furthermore, it is shown that in case of linear control systems the derived dissipation inequality allows to establish a connection to Bode’s Tintegral. Thus the dissipation inequality can be utilized to quantify fundamental performance limitations in feedback design.
Benchmark Examples Stability of Nonlinear ODE’s
, 2007
"... In this section, eight examples will be presented, for which we computed set Lyapunov functions using the method described in this paper. Here the target region TR is the set {x ∈ B: xi − ¯xi  < δ, 1 ≤ i ≤ n}, where B is a given box containing the equilibrium ¯x, and δ> 0 is a arbitrarily gi ..."
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In this section, eight examples will be presented, for which we computed set Lyapunov functions using the method described in this paper. Here the target region TR is the set {x ∈ B: xi − ¯xi  < δ, 1 ≤ i ≤ n}, where B is a given box containing the equilibrium ¯x, and δ> 0 is a arbitrarily given constant. Example 1 A simplified model of a chemical oscillator [2]. ˙x1 = 0.5 − x1 + x 2 1x2