The solvable condition of nonlinear H∞ control problems is given by the Hamilton Jacobi inequality (HJI). The state-dependent Riccati inequality (SDRI) is one of the approaches used to solve the HJI. The SDRI contains the state-dependent coefficient (SDC) form of a nonlinear system. The SDC form is not unique. If a poor SDC form is chosen, then there is no solution for the SDRI. In other words, there exist free parameters of the SDC form that affect the solvability of the SDRI. This study focuses on the free parameters of the SDC form. First, a representation of the free parameters of the SDC form is introduced. The solvability of an SDRI is a sufficient condition for that of the related HJI, and the free parameters affect the conservativeness of the SDRI approach. In addition, a new method for designing the free parameters that reduces the conservativeness of the SDRI approach is introduced. Finally, numerical examples to verify the effect of this method are presented.
The objective of sensor scheduling is to select a sensor (or a group of sensors) from multiple sensors at each time step so as to perform optimally a task based on the sensed data. In this paper, we pose a model predictive type sensor scheduling problem with a general class of criterion functions including the trace, the maximal eigenvalue, and the determinant of the error covariance, for discrete-time linear Gaussian time-varying systems, and develop an approach to solve this problem based on the dynamic programming. We show first that, in a special case of the model predictive deterministic sensor scheduling problem where the Riccati recursion of the error covariance satisfies a specific structural condition, the online optimization using the dynamic programming is reduced to a static optimization, and hence the scheduling algorithm can be easily implemented online. Next, we pose a model predictive stochastic sensor scheduling problem to relax the condition of the deterministic sensor scheduling problem, and show an alternative condition where the optimization is reduced so that the scheduling algorithm can be easily implemented online. Finally, we discuss an example to illustrate the two sensor scheduling algorithms.
This paper considers a method to determine a contact point location between two rigid bodies from a 6-axis force/moment sensor. In the noiseless case, it is well known that the contact point location can be determined directly by solving equations representing the force/moment balances for the exerted force and the resultant sensor signals. Although we can substitute measured signals to the solution whether noise exists or not, if noise exists, a minimizing solution to the error of force/moment balances will be preferable. In this paper, we formulate the estimation problem as a minimization problem of the weighted sum of the error of force/moment balances. The optimization problem is solved analytically and the solution is derived in a closed form. The solution for the noiseless case can be regarded as the minimizing solution for the error of moment balance by assuming that the force balance holds. The proposed method is also extended to the case where the measurement signals for multiple sampling instants can be used. A numerical example and experiments are shown to prove effectiveness of the proposed method.
Based on the analysis of the interaction between a manipulator's hand and a working object, a model representing the constrained dynamics of the robot is first discussed. The constrained forces are expressed by an algebraic function of states, input generalized forces, and the constraint condition, and then a direct position/force controller without force sensor is proposed based on the algebraic relation. To give a grinding system the ability to adapt to any object shape being changed by the grinding, we add a function estimating the constraint condition in real time for the adaptive position/force control. Evaluations through simulations, by fitting the changing constraint surface with spline functions, indicate that reliable position/force control and shape-grinding can be achieved by the proposed controller.
This paper deals with robust control design for linear time-invariant systems by fractional order control (FOC), in which controllers described by differential equations of non-integer orders. The purpose of this paper is to take advantages of the introduction of control parameters and satisfy additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noises. A method for tuning the controller is proposed to fulfill five different design specifications. The specifications on the gain crossover frequency and the phase margin are readily satisfied, together with the damping property of the time response of the controlled system being kept. Simulation results are given to illustrate the effectiveness of this method.
A new identification method with respect to the parameter tuning of a controller is presented. Here, we introduce a virtual two-degree-of-freedom control structure with a feedforward controller described by using a mathematical model of a plant with a tunable parameter. After performing a one-shot experiment, we apply the virtual reference feedback tuning (VRFT), which is a rational and effective tuning method for the parameter of a controller with only one-shot experiment data, to a virtual feedforward controller by using the experimental data obtained in the actual closed loop. We give a condition for a prefilter which is applied to the data to guarantee that the obtained parameter using the VRFT of a controller is close to the desired one. We also show that the prefilter for the identification in the proposed method has a simpler form than that obtained in the normal VRFT for two-degree-of-freedom control scheme. Finally, in order to show the validity of the proposed method, we give an experimental result on the identification of the dynamics of the opening-closing speed of an elevator door.
This paper deals with stability of nonlinear teleoperation systems with time-varying communication delays. The proposed method is the use of passivity-based controllers with time-varying gains which depend on the rate of change of time-varying delay. In our proposed method, the stability condition is independent of the magnitude of the communication delay and the damping of the system. The delay-independent stability is shown via Lyapunov stability methods. Several experimental results show the effectiveness of our proposed teleoperation structure.
A novel approach to identify the unknown time and magnitude of a stepwise or impulsive exogenous input is proposed by introducing an idea of pseudomeasurement with regard to the unknown magnitude. The efficacy of the proposed approach is verified by simulation studies. This paper forms a deterministic counterpart to ones published elsewhere for stochastic systems.
Blind source separation (BSS) is a method for recovering a set of statistically independent signals from the observation of their mixtures without any prior knowledge about the mixing process. If, as a special case, only one source component is to be extracted, it is called blind source extraction (BSE). Since BSE involves a smaller number of parameters to be estimated than BSS, it requires less computation time. In this paper we propose a new algorithm for BSE of the convolutive mixture. The algorithm determines the extractor by evaluating independence between a target signal and other signals. It has some good properties. First, since it is formulated in the time domain, we do not need to worry about the so-called permutation problem. Second, by applying a particular constraint on the extractor the signal quality at the sensors is preserved through the extraction process. A couple of experiments are shown in which the proposed algorithm is applied to the mixture of five voice signals.