Global inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes

Robotica ◽  
2021 ◽  
pp. 1-27
Author(s):  
K. D. Do
Keyword(s):  
Optimal Control ◽  
Mobile Robots ◽  
Tracking Control ◽  
Lévy Processes ◽  
Control Design ◽  
Levy Processes ◽  
Path Tracking ◽  
Tracking Errors ◽  
Hamilton Jacobi Bellman ◽  
And Control

Abstract This paper formulates and solves a new problem of global practical inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes with unknown characteristics. The control design is based on a new inverse optimal control design for nonlinear systems driven by Lévy processes and ensures global practical exponential stability almost surely and in the pth moment for the path-tracking errors. Moreover, it minimizes cost function that penalizes tracking errors and control torques without having to solve a Hamilton–Jacobi–Bellman or Hamilton–Jaccobi–Isaacs equation.

scholarly journals CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

2018 ◽  
Vol 23 (3) ◽  
pp. 390-413 ◽  
Author(s):  
Mario Annunziato ◽  
Hanno Gottschalk
Keyword(s):  
Optimal Control ◽  
Lévy Processes ◽  
Necessary Optimality Conditions ◽  
Functional Space ◽  
Information Criterion ◽  
Estimation Procedure ◽  
Levy Processes ◽  
Parametric Estimation ◽  
L1 Norm ◽  
Control Approach

We present an optimal control approach to the problem of model calibration for Lévy processes based on an non-parametric estimation procedure of the measure. The optimization problem is related to the maximum likelihood theory of sieves [25] and is formulated with the Fokker-Planck-Kolmogorov approach [3, 4]. We use a generic spline discretization of the Lévy jump measure and select an adequate size of the spline basis using the Akaike Information Criterion (AIC) [12]. The first order necessary optimality conditions are derived based on the Lagrange multiplier technique in a functional space. The resulting Partial Integral-Differential Equations (PIDE) are discretized, numerically solved using a scheme composed of Chang-Cooper, BDF2 and direct quadrature methods, jointly to a non-linear conjugate gradient method. For the numerical solver of the Kolmogorov's forward equation we prove conditions for non-negativity and stability in the L1 norm of the discrete solution.

Adaptive and Predictive Path Tracking Control for Off-road Mobile Robots

2007 ◽  
Vol 13 (4) ◽  
pp. 419-439 ◽  
Author(s):  
Roland Lenain ◽  
Benoit Thuilot ◽  
Christophe Cariou ◽  
Philippe Martinet
Keyword(s):  
Mobile Robots ◽  
Tracking Control ◽  
Path Tracking

Optimal Simultaneous Kinematic, Dynamic and Control Design of High Performance Manipulators Based on Trajectory Pattern Method

1998 ◽  
Author(s):  
J. Rastegar ◽  
L. Liu ◽  
M. Mattice
Keyword(s):  
High Speed ◽  
High Performance ◽  
Optimality Criterion ◽  
Control Design ◽  
Tracking Errors ◽  
Motion Patterns ◽  
Trajectory Pattern ◽  
And Control ◽  
Velocity Tracking ◽  
Trajectory Pattern Method

Abstract An optimal simultaneous kinematic, dynamic and control design approach is proposed for high performance computer controlled machines such as robot manipulators. The approach is based on the Trajectory Pattern Method (TPM) and a fundamentally new design philosophy that such machines in general and ultra-high performance machines in particular must only be designed to perform a class or classes of motions effectively. In the proposed approach, given the structure of the manipulator, its kinematic, dynamic and control parameters are optimized simultaneously with the parameters that describe the selected trajectory pattern. In the example presented in this paper, a weighted sum of the norms of the higher harmonics appearing in the actuating torques and the integral of the position and velocity tracking errors are used to form the optimality criterion. The selected optimality criterion should yield a system that is optimally designed to accurately follow the specified trajectory at high speed. Other objective functions can be readily formulated to synthesize systems for optimal performance. The potentials of the developed method and its implementation for generally defined motion patterns are discussed.

Preferences, Utility Function, and Control Design of Complex Cultivation Process

2013 ◽  
pp. 174-198
Keyword(s):  
Optimal Control ◽  
Utility Function ◽  
Kinetic Models ◽  
Control Design ◽  
Monod Kinetics ◽  
Cultivation Process ◽  
Monod Kinetic ◽  
And Control

In the control design are overcome restrictions connected with the observability of the Monod kinetics and with the singularities of the optimal control of Monod kinetic models.

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