Concurrent Learning Adaptive Model Predictive Control with Pseudospectral Implementation

This paper presents a control architecture in which a direct adaptive control technique is used within the model predictive control framework, using the concurrent learning based approach, to compensate for model uncertainties. At each time step, the control sequences and the parameter estimates are both used as the optimization arguments, thereby undermining the need for switching between the learning phase and the control phase, as is the case with hybrid-direct-indirect control architectures. The state derivatives are approximated using pseudospectral methods, which are vastly used for numerical optimal control problems. Theoretical results and numerical simulation examples are used to establish the effectiveness of the architecture.Comment: 21 pages, 13 figure

Nonlinear model predictive low-level control

This dissertation focuses on the development, formalization, and systematic evaluation of a novel nonlinear model predictive control (MPC) concept with derivative-free optimization. Motivated by a real industrial application, namely the position control of a directional control valve, this control concept enables straightforward implementation from scratch, robust numerical optimization with a deterministic upper computation time bound, intuitive controller design, and offers extensions to ensure recursive feasibility and asymptotic stability by design. These beneficial controller properties result from combining adaptive input domain discretization, extreme input move-blocking, and the integration with common stabilizing terminal ingredients. The adaptive discretization of the input domain is translated into time-varying finite control sets and ensures smooth and stabilizing closed-loop control. By severely reducing the degrees of freedom in control to a single degree of freedom, the exhaustive search algorithm qualifies as an ideal optimizer. Because of the exponentially increasing combinatorial complexity, the novel control concept is suitable for systems with small input dimensions, especially single-input systems, small- to mid-sized state dimensions, and simple box-constraints. Mechatronic subsystems such as electromagnetic actuators represent this special group of nonlinear systems and contribute significantly to the overall performance of complex machinery. A major part of this dissertation addresses the step-by-step implementation and realization of the new control concept for numerical benchmark and real mechatronic systems. This dissertation investigates and elaborates on the beneficial properties of the derivative-free MPC approach and then narrows the scope of application. Since combinatorial optimization enables the straightforward inclusion of a non-smooth exact penalty function, the new control approach features a numerically robust real-time operation even when state constraint violations occur. The real-time closed-loop control performance is evaluated using the example of a directional control valve and a servomotor and shows promising results after manual controller design. Since the common theoretical closed-loop properties of MPC do not hold with input moveblocking, this dissertation provides a new approach for general input move-blocked MPC with arbitrary blocking patterns. The main idea is to integrate input move-blocking with the framework of suboptimal MPC by defining the restrictive input parameterization as a source of suboptimality. Finally, this dissertation extends the proposed derivative-free MPC approach by stabilizing warm-starts according to the suboptimal MPC formulation. The extended horizon scheme divides the receding horizon into two parts, where only the first part of variable length is subject to extreme move-blocking. A stabilizing local controller then completes the second part of the prediction. The approach involves a tailored and straightforward combinatorial optimization algorithm that searches efficiently for suboptimal horizon partitions while always reproducing the stabilizing warm-start control sequences in the nominal setup

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.Comment: Submitted to ICRA 2018, 8 page

Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861