Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability

Observer-based fractional-order dynamic terminal sliding mode control of active shock absorbing prostheses for lower limb amputees

Recent biomedical engineering developments have empowered prosthetic devices to evolve from purely mechanical devices to more sophisticated controlled devices, allowing amputees to perform advanced locomotion modes such as passing stairs and walking on sloped surfaces. However, the strongly coupled nonlinear system dynamics make it difficult for the lower-limb prosthesis (LLP) to adapt to complex tasks and isolate the vibrations and acceleration from the residual limb soft tissue. In this regard, realizing the potential of active LLPs to increase user mobility and efficiency requires reliable, stable, and intuitive control strategies to provide a comfortable gait quality. In this study, a fractional-order dynamic terminal sliding mode controller (FDTSMC) is proposed to effectively isolate the residual limb soft tissue from the vibrations and acceleration arising from the pylon and foot. The proposed sliding surfaces guarantee the fast finite-time system states' convergence, and the chattering is remarkably alleviated. Furthermore, since from the practical viewpoint, the actuators are non-ideal and are affected by dead-zone and hysteresis that degrade the LLP's performance, an observer is augmented with the control system to estimate the lumped uncertainties and compensate for the effects of model nonlinear dynamics and disturbances. The closed-loop system stability is ensured in terms of Lyapunov concept. Comparative performance investigations in ideal and non-ideal situations are carried out, and the proposed control scheme's favorable gait shock absorption performance over observer-based conventional SMC and dynamic SMC approaches is revealed.

New pure multi-order fractional optimal control problems with constraints: QP and LP methods

Novel methods for finding the optimal controls of new types of fractional optimal control problems with Riemann-Liouville performance indices and systems comprised of subsystems with Caputo derivatives are introduced. Pure fractional quadratic optimal control problems are modeled as quadratic programming (QP) by using a new idea and a state-control parameterization method. After formulating each linear or nonlinear type, its QP model is derived by which the QP solver in MATLAB can be used to obtain the solutions. There is no need for such operations as defining costate variables, deriving optimality conditions, etc. New concepts such as fractional boundary constraints and Riemann-Liouville isoperimetric constraints, are introduced. Multiple problems in different scenarios are investigated and numerous graphs and numerical results are presented. Pure fractional linear control problems with Riemann-Liouville performance indices and fractional systems are modeled as linear programming (LP) without discretization for the first time. Using the LP solver in MATLAB, the optimal solutions of the fractional/integer linear control problems such as bang-bang (or On-Off) and minimum fuel optimal control systems are obtained. Fractional types of the real-world problems such as container cranes and drug scheduling of cancer chemotherapy, are studied.

Attitude control of a 3-DoF quadrotor platform using a linear quadratic integral differential game approach

In this study, a linear quadratic integral differential game approach is applied to regulate and track the Euler angles for a quadrotor experimental platform using two players. One produces commands for each channel of the quadrotor and another generates the worst disturbance based on the mini-maximization of a quadratic criterion with integral action. For this purpose, first, the attitude dynamics of the platform are modeled and its parameters are identified based on the Nonlinear Least Squares Trust-Region Reflective method. The performance of the proposed controller is evaluated for regulation and tracking problems. The ability of the controller is also examined in the disturbance rejection. Moreover, the influence of uncertainty modeling is studied on the obtained results. Then, the performance of the proposed controller is compared with the classic Proportional Integral Derivative, Linear Quadratic Regulator, and Linear Quadratic Integral Regulator. The results demonstrate the effectiveness of the Game Theory on the Linear Quadratic Regulator approach when the input disturbance occurs.