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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.
Semidefinite Relaxations for Stochastic Optimal Control Policies. arXiv.org
, 2014
"... Abstract — Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild constraint on their disturbances. This has yielded promis ..."
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Abstract — Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild constraint on their disturbances. This has yielded promising directions for research in the planning and control of nonlinear systems. This work proposes a new method obtaining approximate solutions to these linear stochastic optimal control (SOC) problems. A candidate polynomial with variable coefficients is proposed as the solution to the SOC problem. A Sum of Squares (SOS) relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving suboptimality gap. The resulting approximate solutions are shown to be guaranteed over and underapproximations for the optimal value function. I.
Estimating the region of attraction of ordinary differential equations by quantified constraint solving
 In Proceedings of the 3rd WSEAS International Conference on DYNAMICAL SYSTEMS and CONTROL (CONTROL’07
, 2007
"... We formulate the problem of estimating the region of attraction using quantified constraints and show how the resulting constraints can be solved using existing software packages. We discuss the advantages of the resulting method in detail. 1 ..."
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We formulate the problem of estimating the region of attraction using quantified constraints and show how the resulting constraints can be solved using existing software packages. We discuss the advantages of the resulting method in detail. 1
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva60254 Convex Relaxations for Mixed Integer Predictive Control ⋆
"... Convex relaxations for mixed integer predictive ..."
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A Dissipation Inequality for the Minimum Phase Property of Nonlinear Control Systems and Performance Limitations
, 2008
"... 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 d ..."
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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
Proceedings of the International Workshop on the Algorithmic Foundations of Robotics (WAFR), 2004. MultiStep Motion Planning for FreeClimbing Robots
"... Abstract. This paper studies nongaited, multistep motion planning, to enable limbed robots to freeclimb vertical rock. The application of a multistep planner to a real freeclimbing robot is described. This planner processes each of the many underlying onestep motion queries using an incrementa ..."
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Abstract. This paper studies nongaited, multistep motion planning, to enable limbed robots to freeclimb vertical rock. The application of a multistep planner to a real freeclimbing robot is described. This planner processes each of the many underlying onestep motion queries using an incremental, samplebased technique. However, experimental results point toward a better approach, incorporating the ability to detect when onestep motions are infeasible (i.e., to prove disconnection). Current work on a general method for doing this, based on recent advances in computational real algebra, is also presented. 1
CONTRACTION AND SUM OF SQUARES ANALYSIS OF HCCI ENGINES
"... Abstract: By modulating engine valves to reinduct hot exhaust gas together with air and fuel, a clean and ecient form of autoignition can be created. Control of this combustion process, known as homogeneous charge compression ignition (HCCI), requires not only precise valve control but also a combus ..."
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Abstract: By modulating engine valves to reinduct hot exhaust gas together with air and fuel, a clean and ecient form of autoignition can be created. Control of this combustion process, known as homogeneous charge compression ignition (HCCI), requires not only precise valve control but also a combustion control strategy that accounts for the cycletocycle coupling through the exhaust. This paper outlines approaches for proving closedloop stability of a valve controller and combustion controller using nonlinear analysis tools. Stability of the valve controller is shown using contraction analysis. Stability of the combustion controller is shown using sum of squares decomposition, convex optimization and the Positivstellensatz.
Graphs, Simplicial Complexes and Beyond: Topological Tools for Multiagent Coordination
, 2005
"... The ideas developed in this thesis have originated from several distinct events in my student life at Georgia Tech. These events include some thought provoking discussions, frequent travels and collaborations with some very intelligent researchers. The bulk of this work concerns the study of decen ..."
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The ideas developed in this thesis have originated from several distinct events in my student life at Georgia Tech. These events include some thought provoking discussions, frequent travels and collaborations with some very intelligent researchers. The bulk of this work concerns the study of decentralized coordination schemes in large networks of mobile agents, using local interactions. I decided to invest my efforts into this topic after carefully realizing the potential of its applications and the recognition that there has been a lack of a solid mathematical foundation for studying such coordination problems. During the course of this work, several other researchers have focused their attention on this area, and have produced some elegant results. This thesis, however, differs from almost all other works in many respects. The use of topological methods and an emphasis on the relationship