Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults

Abstract

This paper is concerned with the control law synthesis for robot manipulators, which guarantees that the effect of the sensor faults is kept under a permissible level, and ensures the stability of the closed-loop system. Based on Lyapunov’s stability analysis, the conditions that enable the application of the simple bisection method in the optimization procedure were derived. The control law, with certain properties that make the construction of the Lyapunov function much easier—and, thus, the determination of stability conditions—was considered. Furthermore, the optimization problem was formulated as a class of problem in which minimization and maximization of the same performance criterion were simultaneously carried out. The algorithm proposed to solve the related zero-sum differential game was based on Newton’s method with recursive matrix relations, in which the first- and second-order derivatives of the objective function are calculated using hyper-dual numbers. The results of this paper were evaluated in simulation on a robot manipulator with three degrees of freedom.

Application of Multi-Criteria Optimization Methods in the Calibration Process of Digital Measuring Instruments

“…In the min–max method, one searches for such parameter values for which individual objective functions give the values of the result parameters that are the same while, at the same time, as small as possible, from the extremes of both objective functions (approximate solution), i.e., those for which the increases and the decreases of both objective functions are the same and as small as possible [ 42 ].…”

Optimized leader‐follower consensus control using combination of reinforcement learning and sliding mode mechanism for multiple robot manipulator system

“…As indication above, the optimal distributed control 𝜏 * k must solely satisfy the optimal performance function (20). Therefore, it is identified as the sole solution for the distributed HJB equation (21).…”

“…18 Furthermore, optimal control of multiple manipulator system has become one of the hot academic topics, and some important results have been obtained. 19,20 Nevertheless, since, for achieving the cooperation, such a control needs to couple the states of neighbor manipulator relevant with communication topology, the algorithm complexity is greatly increased.…”

“…It is worth mentioning that the multi‐manipulator system has gained significant attention and application because it can collaborate to complete some large and complex tasks to surpass the capability summation of multiple individual manipulators 18 . Furthermore, optimal control of multiple manipulator system has become one of the hot academic topics, and some important results have been obtained 19,20 . Nevertheless, since, for achieving the cooperation, such a control needs to couple the states of neighbor manipulator relevant with communication topology, the algorithm complexity is greatly increased.…”

Playing Extensive Games with Learning of Opponent’s Cognition

“…Decision-making is a basic component of various agents' behaviors [1], such as Autonomous driving and sensor systems [2], and has been studied in many fields such as psychology, economics, and artificial intelligence due to its ubiquitousness [3,4]. One's cognition plays a crucial role in decision-making processes and outcomes, since available alternatives can be identified and weighed effectively only when meaningful information is collected.…”