Efficient simulation and optimization of differential algebraic equations on embedded hardware for control.

Dynamic optimization based control and estimation techniques have gained increasing popularity, because of their ability to treat a wide range of problems and applications. They rely on the explicit formulation of a cost function, which needs to be minimized given the constraints of the problem and the system dynamics. Especially in the context of real-time applications of control and estimation on embedded hardware, the computational burden associated with the online solution of the optimal control problem forms the main limiting factor in the deployment of such an advanced strategy.

For that purpose, this thesis considers the development of tailored algorithms of simulation methods for embedded optimization that allows for an efficient implementation of nonlinear model predictive control (NMPC) or moving horizon estimation (MHE). A direct treatment of the optimal control problem requires the numerical simulation of the continuous time nonlinear dynamics and the solution of the resulting large but structured optimization problem. We additionally propose a new format to define the dynamic model, which allows one to directly exploit the present structure of linear or partially linear subsystems in the formulation of the system dynamics. In addition, we also discuss embedded optimization algorithms for a more general set of interconnected subsystems based on a distributed multiple shooting technique.

As we focus on Newton-type optimization algorithms, it is important to extend the numerical simulation method with an efficient propagation of its first and possibly higher order derivative information. We discuss the tailored implementation of such a sensitivity analysis for both explicit and implicit integration, such as the collocation methods that form a specific family of implicit Runge-Kutta schemes. In addition, a novel Hessian propagation scheme is proposed for both a discrete and continuous time sensitivity analysis, which allows one to maintain and exploit the symmetry of the second order derivatives. Based on these symmetric sensitivity equations, an alternative three-sweep propagation (TSP) technique is presented and analyzed.

When embedding an implicit integration scheme within a direct multiple shooting based Newton-type optimization algorithm, one ends up with an outer and inner level of iterations which is typically not the most efficient computational approach. We therefore propose an alternative implementation, which we refer to as a lifted collocation integrator, and discuss its advantages and disadvantages compared to multiple shooting and direct collocation. Two alternative extensions to inexact Newton based optimization are presented, using either an adjoint differentiation technique or an iterative sensitivity propagation. We establish new theoretical results on the local convergence of this inexact Newton scheme with iterated sensitivities. Unlike for previously existing algorithms, we show that local convergence for the inner scheme is necessary and often also sufficient for asymptotic contraction of the new proposed optimization method.

In addition to the use of tailored optimal control algorithms, the performance of embedded applications strongly relies on efficient code implementations. This thesis therefore includes an implementation of the major new algorithmic techniques as part of the automatic code generation tool within the open-source ACADO Toolkit software package. We discuss some of the main real-world control applications that were made possible using such an ACADO code generated solver. More specifically, we discuss the airpath control for a two-stage turbocharged gasoline engine in more detail. The resulting NMPC scheme on the dSpace MicroAutoBox is shown to meet the challenging demands of this control application, with a sampling time of 25 ms. It is validated based on closed-loop simulations as well as in-vehicle experimental results.