Control of Constrained Nonlinear Systems
Though significant progress has been made in the field of control theory, its practical application is sometimes hindered by the failure to account for physical constraints. Constraints dominate the majority of real-time control challenges. In daily life, there are lots of uncertain dynamic systems where constraints appear in different forms, such as performance, saturation, physical stoppages, and safety specifications. For such systems, while designing the controller in real time, the constraints are ineludible.
To design a controller for such systems, we use tools like Control Barrier Function (CBF), Prescribed Performance Control and Barrier Lyapunov Function (BLF). Further, to deal with the unknown dynamics of the systems, we work on approximation-free techniques. Following are the few important results.
Approximation-free Prescribed Performance Control with Prescribed Input Constraints: We proposed a controller for the tracking problem of control affine nonlinear system subjected to output and input constraints. The structure of the controller is simple as it does not require any adaptive laws, calculation of any derivatives, system knowledge or approximation. In short, the controller is easy to implement and an approximation-free controller. Also, we have derived the feasibility condition for the prescription of constraint restricts arbitrary prescription. In future, the work will be extended for multi-agent systems.
Formal Verification and Synthesis using Barrier Functions: We provide systematic verification and synthesis of (stochastic) control systems against high-level specifications. Also, we proposed a compositional framework for constructing barrier functions to improve the scalability of the approach to large-scale interconnected systems.
P. K. Mishra and P. Jagtap, Approximation-free Prescribed Performance Control with Prescribed Input Constraints, Submitted for publication. [preprint]
P. K. Mishra and P. Jagtap, On Controller Design for Unknown Nonlinear Systems with Prescribed Performance and Input Constraints, accepted at The Indian Control Conference (ICC) 2022
P. Jagtap and D. V. Dimarogonas, Consensus Control of Stochastic Multi-agent Systems with Prescribed Performance Constraints, The 60th IEEE Conference on Decision and Control (CDC) 2021 [preprint], [link]