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Models for Multi-Specie Chemical Reactions Using Polynomial Stochastic Hybrid Systems

Models for Multi-Specie Chemical Reactions Using Polynomial ...

引用

IEEE Conference on Decision and control

作者： A. Singh J.P. Hespanha Center for Control Engineering and Computation University of California Santa Barbara CA USA

A procedure for constructing approximate stochastic models for chemical reactions is presented. This is done by representing the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). An important property of pSHSs is that the dynamics of all the statistical moments of its continuous states, evolves according to a infinite-dimensional linear ordinary differential equation (ODE). Under appropriate conditions, this infinite-dimensional ODE can be accurately approximated by a finite-dimensional nonlinear ODE, the state of which typically contains the moments of interest. In this paper, for a very general class of chemical reactions, we provide existence and uniqueness conditions for these finite-dimensional nonlinear ODEs. Furthermore, explicit formulas to construct them are also provided. To illustrate the applicability of our results, we construct an approximate stochastic model for a decaying and dimerizing chemical reaction set. Moment estimates obtained from the finite-dimensional nonlinear ODE are compared with estimates obtained from a large number of Monte Carlo simulations.

关键词： Chemicals Polynomials Stochastic systems Stochastic processes Differential equations Vectors Nonlinear dynamical systems Kinetic theory Probability density function Biological materials

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Monitoring driver's alertness based on the driving performance estimation and the EEG power spectrum analysis

Monitoring driver's alertness based on the driving performan...

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27th Annual International Conference of the IEEE-engineering-in-Medicine-and-Biology-Society

作者： Liang, S. F. Lin, C. T. Wu, R. C. Chen, Y. C. Huang, T. Y. Jung, T. P. Brain Research Center University System of Taiwan Taiwan Department of Electrical and Control Engineering National Chiao-Tung University Hsinchu Taiwan Institute for Neural Computation University of California San Diego San Diego CA United States

ISBN: (纸本)0780387406

Preventing accidents caused by drowsiness behind the steering wheel is highly desirable but requires techniques for continuously estimating driver's abilities of perception, recognition and vehicle control abilities. This paper proposes methods for drowsiness estimation that combine the electroencephalogram (EEG) log subband power spectrum, correlation analysis, principal component analysis, and linear regression models to indirectly estimate driver's drowsiness level in a virtual-reality-based driving simulator. Results show that it is feasible to quantitatively monitor driver's alertness with concurrent changes in driving performance in a realistic driving simulator.

关键词： alertness EEG power spectrum correlation analysis linear regression model

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Results on solution sets to hybrid systems with applications to stability theory

Results on solution sets to hybrid systems with applications...

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American control Conference (ACC)

作者： R. Goebel A.R. Teel Seattle WA USA Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara USA

Motivated by questions in stability theory for hybrid dynamical systems, we establish some fundamental properties of the set of solutions to such systems. Using the notion of a hybrid time domain and general results on set and graphical convergence, we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and "upper semicontinuous" with respect to initial conditions and system perturbations. The latter means that each solution to the system under perturbations is close to some solution of the unperturbed system on a compact hybrid time domain. The general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets. For example, it is shown that the basin of attraction for a compact attractor is (relatively) open, the attractivity is uniform from compact subsets of the basin of attraction, and asymptotic stability is robust with respect to small perturbations.

关键词： Robust stability Asymptotic stability control engineering control engineering computing Military computing Nonlinear control systems control systems Robust control Nonlinear systems Differential equations

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Fractal Graph Optimization Algorithms

Fractal Graph Optimization Algorithms

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IEEE Conference on Decision and control

作者： J.R. Riehl J.P. Hespanha Center for Control Dynamical Systems and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

We introduce methods of hierarchically decomposing three types of graph optimization problems: all-pairs shortest path, all-pairs maximum flow,and search. Each method uses a partition on the graph to create a high level problem and several lower level problems. The computations on each level are identical, so the low level problems can be further decomposed. In this way, the problems become fractal in nature. We use these decomposition methods to establish upper and lower bounds on the optimal criteria of each problem, which can be achieved with much less computation than what is required to solve the original problem. Also, for each problem, we find an optimal number of partitions that minimizes computation time. As the number of hierarchical levels increases, the computational complexity decreases at the expense of looser bounds.

关键词： Fractals Partitioning algorithms Shortest path problem Search problems Navigation Path planning Costs Dynamic programming Optimization methods computational complexity

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On hybrid controllers that induce input-to-state stability with respect to measurement noise

On hybrid controllers that induce input-to-state stability w...

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IEEE Conference on Decision and control

作者： R.G. Sanfelice A.R. Teel Center for Control Dynamical Systems and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

For a class of nonlinear systems affine in controls and with unknown high frequency gain, we develop a hybrid control strategy that guarantees (practical) global input-to-state stability (ISS) with respect to measurement noise. We provide a design procedure for the hybrid controller and apply it to Freeman’s counterexample and minimum-phase relative degree one systems.

关键词： Stability Noise measurement control systems Feedback Nonlinear control systems Nonlinear systems Noise robustness Frequency measurement Gain measurement Robust control

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Continuous time constrained linear quadratic regulator - convex duality approach

Continuous time constrained linear quadratic regulator - con...

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American control Conference (ACC)

作者： R. Goebel M. Subbotin Seattle WA USA Center for Control Engineering and Computation ECE Dept University of California Santa Barbara CA USA

A continuous time infinite horizon linear quadratic regulator with input constraints is studied. On the theoretical side, optimality conditions, both in the open loop and feedback form, are shown together with smoothness of the value function and local Lipschitz continuity of the optimal feedback. Arguments are self-contained, use basic ideas of convex conjugacy, and in particular, use a dual optimal control problem. A method of calculating the optimal and stabilizing feedback without relying on discrete optimization is outlined.

关键词： Time factors Regulators Optimal control Infinite horizon Feedback loop Linear systems Constraint optimization Riccati equations control engineering control engineering computing

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Results on convergence in hybrid systems via detectability and an invariance principle

Results on convergence in hybrid systems via detectability a...

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American control Conference (ACC)

作者： R.G. Sanfelice R. Goebel A.R. Teel Center for Control Eng. & Compulation California Univ. Santa Barbara CA USA Center for Control Engineering and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

Two invariance principles for generalized hybrid systems are presented. One version involves the use of a nonincreasing function, like in the original work of LaSalle. The other version involves "meagreness" conditions. These principles characterize asymptotic convergence of bounded hybrid trajectories to weakly invariant sets. A detectability property is used to locate a set in which the Q-limit set of a trajectory is contained. Next, it is shown how the invariance principles can be used to certify asymptotic stability in hybrid systems. Lyapunov and Krasovskii theorems for hybrid systems are included.

关键词： Convergence Asymptotic stability Military computing Sufficient conditions Mathematical model Difference equations control engineering control engineering computing Linear systems Nonlinear systems

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Path-following Approach to control Effort Reduction of Tracking Feedback Laws

Path-following Approach to Control Effort Reduction of Track...

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IEEE Conference on Decision and control

作者： D.B. Dacic M.V. Subbotin P.V. Kokotovic Department of Electrical and Electronic Engineering University of Melbourne VIC Australia Center for Control Dynamic Systems and Computation University of California Santa Barbara CA USA

We develop a path-following algorithm for redesign of tracking feedback laws to reduce the control effort. Our algorithm provides a tradeoff between the control effort and the dynamic performance along the path, while maintaining the desired convergence to the path. It is applicable to feedback linearizable systems with stable zero dynamics. We illustrate it on a realistic hovercraft model, and compare the resulting control effort with control efforts of other path-following and tracking algorithms.

关键词： Vehicle dynamics Convergence control systems Motion control State feedback Motion measurement Vehicles Airplanes Robots Tracking

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On Traveling Salesperson Problems for Dubins ’ vehicle: stochastic and dynamic environments

On Traveling Salesperson Problems for Dubins ’ vehicle: sto...

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IEEE Conference on Decision and control

作者： K. Savla F. Bullo E. Frazzoli Francesco Bullo are with the Center for Control Dynamical Systems and Computation University of California슠Santa Barbara USA Mechanical and Aerospace Engineering Department University of California Los Angeles USA

In this paper we propose some novel planning and routing strategies for Dubins’ vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly sampled from a uniform distribution in a rectangle, what is the shortest Dubins'tour through the targets and what is its length? We show that the expected length of such a tour is Ω(n m=2/3 )and we propose a novel algorithm that generates a tour of length O(n m=2/3 log(n) m=1/3 ) with high probability. Second, we study a dynamic version of the TSP (known as "Dynamic Traveling Repairperson Problem" in the Operations Research literature): given a stochastic process that generates targets, is there a policy that allows a Dubins vehicle to stabilize the system, in the sense that the number of unvisited targets does not diverge over time? If such policies exist, what is the minimum expected waiting period between the time a target is generated and the time it is visited? We propose a novel receding-horizon algorithm whose performance is almost within a constant factor from the optimum.

关键词： Stochastic processes Vehicle dynamics Unmanned aerial vehicles Approximation algorithms Polynomials Path planning Operations research Strategic planning Routing Mathematics

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On collective motion in sensor networks: sample problems and distributed algorithms

On collective motion in sensor networks: sample problems and...

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IEEE Conference on Decision and control

作者： A. Ganguli S. Susca S. Martinez F. Bullo J. Cortes Department of Mechanical and Environmental Engineering University of California슠Santa Barbara Santa Barbara CA USA Coordinated Science Laboratory University of Illinois Urbana-Champaign Urbana IL USA Department of Mechanical and Environmental Engineering and with the Center for Control Dynamical Systems and Computation University of California슠Santa Barbara Santa Barbara CA USA Department of Applied Mathematics and Statistics University of California Santa Cruz Santa Cruz CA USA

Adopting a tutorial approach, this paper surveys some control and systems theory problems that have recently gained interest in the context of multi-vehicle and sensor networks. By means of illustrative examples, we discuss some challenges in modeling of robotic networks, motion coordination algorithms, sensing and estimation tasks, and complexity of distributed algorithms.

关键词： Intelligent networks Distributed algorithms Robot kinematics Robot sensing systems Sensor systems Sensor phenomena and characterization Marine animals Target tracking control systems Biosensors

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