Offset-free receding horizon control of constrained linear systems

The design of a dynamic state feedback receding horizon controller is addressed, which guarantees robust constraint satisfaction, robust stability and offset-firee control of constrained linear systems in the presence of time-varying setpoints and unmeasured disturbances. This objective is obtained by first designing a dynamic linear offset-free controller and computing an appropriate domain of attraction for this controller. The linear (unconstrained) controller is then modified by adding a perturbation term, which is computed by a (constrained) robust receding horizon controller. The receding horizon controller has the property that its domain of attraction contains that of the linear controller. In order to ensure robust constraint satisfaction, in addition to offset-free control, the transient, as well as the limiting behavior of the disturbance and setpoint need to be taken into account in the design of the receding horizon controller. The fundamental difference between the results and the existing literature on receding horizon control is that the transient effect of the disturbance and set point sequences on the so-called "target calculator" is explicitly incorporated in the formulation of the receding horizon controller. An example of the control of a continuous stirred-tank reactor is presented. (c) 2005 American Institute of Chemical Engineers

Robust and Safe Autonomous Navigation for Systems with Learned SE(3) Hamiltonian Dynamics

Stability and safety are critical properties for successful deployment of automatic control systems. As a motivating example, consider autonomous mobile robot navigation in a complex environment. A control design that generalizes to different operational conditions requires a model of the system dynamics, robustness to modeling errors, and satisfaction of safety \NEWZL{constraints}, such as collision avoidance. This paper develops a neural ordinary differential equation network to learn the dynamics of a Hamiltonian system from trajectory data. The learned Hamiltonian model is used to synthesize an energy-shaping passivity-based controller and analyze its \emph{robustness} to uncertainty in the learned model and its \emph{safety} with respect to constraints imposed by the environment. Given a desired reference path for the system, we extend our design using a virtual reference governor to achieve tracking control. The governor state serves as a regulation point that moves along the reference path adaptively, balancing the system energy level, model uncertainty bounds, and distance to safety violation to guarantee robustness and safety. Our Hamiltonian dynamics learning and tracking control techniques are demonstrated on \Revised{simulated hexarotor and quadrotor robots} navigating in cluttered 3D environments

Model-based and Koopman-based predictive control:a braking control systems comparison

Anti-locking Braking systems are crucial safety systems in modern vehicles. In this work, we investigate the possibility to use Model Predictive Control (MPC) for braking systems by considering three different models identified from data. Specifically, we consider two models, whose structure and the identification procedure are driven by physics principles, and a third black-box modeling approach that relies on Koopman theory. By comparing the effectiveness of the three resulting MPC schemes in a high-fidelity simulation environment, we show that Koopman-based MPC can generally be a viable solution for the design of braking controllers, which might not be the case of nonlinear MPC or approximated scheme like the second one we test.</p

Developments in Stochastic Fuel Efficient Cruise Control and Constrained Control with Applications to Aircraft.

This dissertation presents contributions to fuel-efficient control of vehicle speed and constrained control with applications to aircraft. In the first part of this dissertation a stochastic approach to fuel-efficient vehicle speed control is developed. This approach encompasses stochastic modeling of road grade and traffic speed and uses the application of stochastic dynamic programming to generate vehicle speed control policies that are optimized for the trade-off between fuel consumption and travel time. It is shown that the policies lead to the emergence of time-varying vehicle speed patterns, often referred to as pulse and glide (PnG). Through simulations and experiments it is confirmed that these time-varying vehicle speed profiles are more fuel-efficient than driving at a comparable constant speed. A practical implementation strategy of these patterns is then developed and demonstrated. Also, several additional contributions are made to approaches for stochastic modeling of road grade and vehicle speed that include the use of Kullback-Liebler divergence and divergence rate and a stochastic jump-like model for the behavior of the road grade. In the second part of the dissertation, contributions to constrained control with applications to aircraft are described. Recoverable sets and integral safe sets of initial states of constrained closed-loop systems are introduced first and computational procedures of such sets based on linear discrete-time models are given. An approach to constrained flight planning based on chaining recoverable sets or integral safe sets is described and illustrated with a simulation example. Finally, two control schemes that exploit integral safe sets are proposed. The first scheme, referred to as the controller state governor (CSG), resets the controller state (typically an integrator) to enforce the constraints and enlarge the set of plant states that can be recovered without constraint violation. The second scheme, referred to as the controller state and reference governor (CSRG), combines the controller state governor with the reference governor control architecture and provides the capability of simultaneously modifying the reference command and the controller state to enforce the constraints. Theoretical results that characterize the response properties of both schemes are presented. Examples are reported that illustrate the operation of these schemes.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111399/1/kevinmcd_1.pd

Low Complexity Model Predictive Control of a Diesel Engine Airpath.

The diesel air path (DAP) system has been traditionally challenging to control due to its highly coupled nonlinear behavior and the need for constraints to be considered for driveability and emissions. An advanced control technology, model predictive control (MPC), has been viewed as a way to handle these challenges, however, current MPC strategies for the DAP are still limited due to the very limited computational resources in engine control units (ECU). A low complexity MPC controller for the DAP system is developed in this dissertation where, by "low complexity," it is meant that the MPC controller achieves tracking and constraint enforcement objectives and can be executed on a modern ECU within 200 microseconds, a computation budget set by Toyota Motor Corporation. First, an explicit MPC design is developed for the DAP. Compared to previous explicit MPC examples for the DAP, a significant reduction in computational complexity is achieved. This complexity reduction is accomplished through, first, a novel strategy of intermittent constraint enforcement. Then, through a novel strategy of gain scheduling explicit MPC, the memory usage of the controller is further reduced and closed-loop tracking performance is improved. Finally, a robust version of the MPC design is developed which is able to enforce constraints in the presence of disturbances without a significant increase in computational complexity compared to non-robust MPC. The ability of the controller to track set-points and enforce constraints is demonstrated in both simulations and experiments. A number of theoretical results pertaining to the gain scheduling strategy is also developed. Second, a nonlinear MPC (NMPC) strategy for the DAP is developed. Through various innovations, a NMPC controller for the DAP is constructed that is not necessarily any more computationally complex than linear explicit MPC and is characterized by a very streamlined process for implementation and calibration. A significant reduction in computational complexity is achieved through the novel combination of Kantorovich's method and constrained NMPC. Zero-offset steady state tracking is achieved through a novel NMPC problem formulation, rate-based NMPC. A comparison of various NMPC strategies and developments is presented illustrating how a low complexity NMPC strategy can be achieved.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120832/1/huxuli_1.pd

Extremum-Seeking Guidance and Conic-Sector-Based Control of Aerospace Systems

This dissertation studies guidance and control of aerospace systems. Guidance algorithms are used to determine desired trajectories of systems, and in particular, this dissertation examines constrained extremum-seeking guidance. This type of guidance is part of a class of algorithms that drives a system to the maximum or minimum of a performance function, where the exact relation between the function's input and output is unknown. This dissertation abstracts the problem of extremum-seeking to constrained matrix manifolds. Working with a constrained matrix manifold necessitates mathematics other than the familiar tools of linear systems. The performance function is optimized on the manifold by estimating a gradient using a Kalman filter, which can be modified to accommodate a wide variety of constraints and can filter measurement noise. A gradient-based optimization technique is then used to determine the extremum of the performance function. The developed algorithms are applied to aircraft and spacecraft. Control algorithms determine which system inputs are required to drive the systems outputs to follow the trajectory given by guidance. Aerospace systems are typically nonlinear, which makes control more challenging. One approach to control nonlinear systems is linear parameter varying (LPV) control, where well-established linear control techniques are extended to nonlinear systems. Although LPV control techniques work quite well, they require an LPV model of a system. This model is often an approximation of the real nonlinear system to be controlled, and any stability and performance guarantees that are derived using the system approximation are usually void on the real system. A solution to this problem can be found using the Passivity Theorem and the Conic Sector Theorem, two input-output stability theories, to synthesize LPV controllers. These controllers guarantee closed-loop stability even in the presence of system approximation. Several control techniques are derived and implemented in simulation and experimentation, where it is shown that these new controllers are robust to plant uncertainty.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143993/1/aexwalsh_1.pd