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This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances. By using an approach based on the guaranteed cost control theory, a technique is proposed to design a state feedback controller ensuring for the closed-loop system: (i) the local exponential stability of the zero equilibrium point; (ii) the inclusion of a given region into the domain of exponential stability of the equilibrium point; (iii) the satisfaction of a guaranteed level of performance, in terms of boundedness of some optimality indexes. In particular, a sufficient condition for the existence of a state feedback controller satisfying a prescribed integral–quadratic index is provided, followed by a sufficient condition for the existence of a state feedback controller satisfying a given L 2 -gain disturbance rejection constraint. By the proposed design procedures, the optimal control problems dealt with here can be efficiently solved as Linear Matrix Inequality (LMI) optimization problems.

In this paper, the tracking control problem of a biomimetic exoskeleton powered by a pair of pneumatic artificial muscles is considered. The antagonistic configuration of the pair of pneumatic muscles, which is biologically inspired, enables safe and reliable actuation in applications of orthopaedic rehabilitation. However, during the inflation-deflation process, the pneumatic muscles introduce nonlinearity and hysteresis which deteriorate the control performance. A model of the antagonistic artificial muscles is adopted to develop a computed-torque control for feedforward compensation of the nonlinear dynamics of the actuated joint. A PID control action is used in combination with the feedforward compensation to achieve fast and accurate tracking control performance. The model, which possesses a reduced set of parameters as functions of the inflation/deflation phase, enables efficient nonlinear compensation. The experimental tests on the biomechatronic device, compared with other state-of-the-art approaches for controlling pneumatic artificial muscles, show better tracking performance in terms of convergence rate and robustness, justifying the convenience of using the proposed control methodology in the design of tracking controllers for exoskeletal biomechatronic devices.

A novel dynamic friction model, which allows to capture friction hysteresis with non-local memory, is presented in this paper. The model is conceived in order to find a trade-off between accuracy of the model prediction and difficulty of implementation in motion control systems with model-based friction compensation. The hysteresis function introduced into the model accounts for non-local memory, i.e., the property for which the friction output depends not only on the initial conditions but also on past extremum values of the input or the output. In comparison with other models incorporating a hysteresis function with non-local memory, the proposed model is demonstrated to reduce the number of parameters necessary to reproduce the hysteresis loops observed experimentally. Moreover, parameter identification can benefit from the availability of a closed form of the model solution.

The problem of the robust and optimal control for uncertain quadratic systems is dealt with in this paper. Resorting to a guaranteed cost approach, this paper proposes a novel control design methodology which enables to find a state feedback controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point; iii) the satisfaction of a quadratic performance index. The control performance is guaranteed against parametric uncertainties which are assumed to be norm-bounded. This design procedure involves the solution of a Linear Matrix Inequalities (LMIs) optimization problem, which can be efficiently solved via off-the-shelf algorithms. An example, concerning an application of motion control for robotic arms, shows the effectiveness of the proposed methodology.

This paper deals with the problem of the stabilization of uncertain quadratic systems via state feedback. The main contribution of the paper is a control design methodology which enables to find a robust controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point. This design procedure involves the solution of a Linear Matrix Inequalities (LMIs) feasibility problem, which can be efficiently solved via available optimization algorithms. A numerical example shows the effectiveness of the proposed methodology.

In this paper, a robust and optimal control problem for uncertain bilinear systems is formulated via a guaranteed-cost approach and then applied to tracking control design of a robotic arm actuated by Pneumatic Artificial Muscles (PAMs). Taking into account the nonlinear dynamics of the pneumatic actuators, the tracking error dynamics has been described as an uncertain bilinear systems, whereas unknown perturbations on robot dynamics and modelling mismatch are regarded as an external disturbance to be attenuated. Some numerical simulations are also given to demonstrate both robustness and optimality of the control performance in tracking desired trajectories with the required accuracy.

This paper addresses the problem of designing a guaranteed cost controller for continuous-time nonlinear quadratic systems. The main result is a sufficient condition for the existence of a linear state feedback controller achieving an assigned guaranteed cost, whenever the state trajectories remain within a suitable invariant set. The conditions are cast in the form of Linear Matrix Inequalities (LMIs), which can be efficiently solved via available optimization algorithms. The effectiveness of the devised approach is illustrated through an example concerning the attitude control of an unmanned aerial vehicle.

Through a lumped parameter modelling approach, a dynamical model, which can reproduce the motion of the muscles of a human body standing in different postures during Whole Body Vibrations (WBVs) treatment, has been developed. The key parameters, associated to the dynamics of the motion of the muscles of the lower limbs, have been identified starting from accelerometer measurements. The developed model can be usefully applied to the optimization of WBVs treatments which can effectively enhance muscle activation.

In this paper, an optimal control problem for uncertain bilinear systems is formulated via a guaranteed cost approach and then applied to the design of a stabilizing controller for a robot arm actuated by Pneumatic Artificial Muscles (PAMs). The results show that the contributed methodology is suitable for efficiently designing control systems which can match the requirements both on safety and on energy efficiency for PAMs-driven robots during human-robot interactions. The performances of the state-feedback control system are evaluated on the basis of some numerical simulations.