Sadjaad Ozgoli

Sina Sanjari, Sadjaad Ozgoli

This paper presents an approach to systematically design sliding mode control and manifold to stabilize nonlinear uncertain systems. The objective is also accomplished to enlarge the inner bound of region of attraction for closed-loop dynamics. The method is proposed to design a control that guarantees both asymptotic and finite time stability given helped by (bilinear) sum of squares programming. The approach introduces an iterative algorithm to search over sliding mode manifold and Lyapunov function simultaneity. In the case of local stability it concludes also the subset of estimated region of attraction for reduced order sliding mode dynamics. The sliding mode manifold and the corresponding Lyapunov function are obtained if the iterative SOS optimization program has a solution. Results are demonstrated employing the method for several examples to show potential of the proposed technique.

Jafar Kazemi, Sadjaad Ozgoli

Lower extremity exoskeleton has been developed as a motion assistive technology in recent years. Walking pattern generation is a fundamental topic in the design of these robots. The usual approach with most exoskeletons is to use a pre-recorded pattern as a look-up table. There are some deficiencies with this method, including data storage limitation and poor regulation relating to the walking parameters. Therefore modeling human walking patterns to use in exoskeletons is required. The few existing models provide piece by piece walking patterns, only generating at the beginning of each stride cycle in respect to fixed walking parameters. In this paper, we present a real-time walking pattern generation method which enables changing the walking parameters during the stride. For this purpose, two feedback controlled third order systems are proposed as optimal trajectory planners for generating the trajectory of the x and y components of each joints position. The boundary conditions of the trajectories are obtained according to some pre-considered walking constraints. In addition, a cost function is intended for each trajectory planner in order to increase the trajectories smoothness. We use the minimum principle of Pontryagin to design the feedback controller in order to track the boundary conditions in such a way that the cost functions are minimized. Finally, by using inverse kinematics equations, the proper joints angles are generated for and implemented on Exoped robot. The good performance of the gait planner is demonstrated by second derivative continuity of the trajectories being maintained as a result of a simulation, and user satisfaction being determined by experimental testing.

S. Sanjari, S. Ozgoli

Finite time analysis of the continuous system is investigated through both stability and stabilization based on Sum of squares programming. A systematic approach is proposed to construct Lyapunov function and Control Lyapunov function for this objective. The Region of reaching, the set which has the property that all trajectories starting from initial point inside it reach to the origin in finite time, is introduced, and The largest subset of region of reaching is estimated using Lyapunov based technique. The main results are presented to give sufficient conditions which can be translated by semi-definite program. These conditions are provided a feasibility problem involving sum of squares constraints. The results of the paper are then verified by several simulation and numerical examples. Furthermore, one important practical application namely as a super twisting second order sliding mode control also is presented using the proposed result to illustrate its effectiveness.

S. Sanjari, S. Ozgoli

This paper presents a general form of integral sliding mode manifold, and proposes an algorithmic approach based on Sum of Squares (SOS) programming to design generalized integral sliding mode manifold and controller for nonlinear systems with both matched and unmatched uncertainties. The approach also gives a sufficient condition for successful design of controller and manifold parameters. The result of the paper is then verified by several simulation examples and two practical applications, namely Glucose-insulin regulation problem and the unicycle dynamics steering problem are considered.