Nonlinear Optimal Control
Receding-horizon optimal control techniques, such as nonlinear model-predictive control, are a powerful methodology when aggressive control inputs are necessary but strict state and input constraints are to be imposed. Here, the control feedback signal is subject to the online solution of a constrained optimization problem, of which a solution in any case can usually not be guaranteed.
I am developing techniques to determine feasibility and ensure convergence of an optimizer either in the design phase or during run-time.
In linear control theory, systems are either stable or unstable. For many physical applications, however, this is hardly the case. Aircraft flight beyond stall, for example, is characterized by nonlinear and locally unstable. In these cases, knowledge about the region of attraction of a selected trim condition can be important.
Using sum-of-squares programming and Lyapunov theory, I have estimated the region of attraction of piecewise aircraft dynamics and synthesize control feedback laws for deep-stall recovery subject to state and input constraints. Furthermore, I have developed an algorithm to efficiently analyze multivariate splines.
I am now studying different approaches to size a region of attraction estimate and work on a general framework for the different systems. I am further interested in techniques to tackle the resulting bilinear sum-of-squares constraints.
During my work on upset recovery, I have found polynomial fits unsuitable to model full-envelope aircraft dynamics accurately, in particular for flight beyond the stall angle of attack. Therefore, I have developed models of the aerodynamic coefficients which are defined by piecewise polynomials, representing dynamics before and after stall. (The toolbox
pwpfit is now available open-source.) These piecewise models do not only provide better fitting, and have been successfully used for model-predictive upset recovery control, but they also allow for (and led to the development of) sum-of-squares based analysis methods which have previously been presented for polynomial systems.
Hybrid systems (also hybrid automata or hybrid models) are a very general framework, that account for almost any cyber-physical application. This generality, however, also is their weakness and analysis of hybrid system properties, such as stability and safety, often is challenging.
Nonlinear systems often manifest in multiple equilibrium conditions and number of stability of these equilibria may change with variations in the system inputs. Continuing the trim conditions of an aircraft, for example, along the possible surface deflections, one can study the steady-state characteristics of the aircraft in upset conditions such as post-stall, spirals, or oscillatory spin.
Flapping-wing-driven aviation is perhaps humanity's oldest dream but became obsolete with the advent of fixed-wing aircraft. Due to remote-piloted and autonomous micro air vehicles (MAV), the bird-like flight has seen a revival in this century for its potential to combine the agility of rotorcraft with the efficiency of airplanes. For my Master's thesis, I have developed and tested a position control law for a flapping-wing MAV in a wind-tunnel.