Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints

In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of time-varying monotonically increasing stage cost penalty. The main result is that the $0$-reachability prediction horizon can always be made stabilizing provided that the increasing rate of the penalty is made sufficiently high.Comment: Submitted to Automatic

High-Speed Obstacle Avoidance at the Dynamic Limits for Autonomous Ground Vehicles

Enabling autonomy of passenger-size and larger vehicles is becoming increasingly important in both military and commercial applications. For large autonomous ground vehicles (AGVs), the vehicle dynamics are critical to consider to ensure vehicle safety during obstacle avoidance maneuvers especially at high speeds. This research is concerned with large-size high-speed AGVs with high center of gravity that operate in unstructured environments. The term `unstructured' in this context denotes that there are no lanes or traffic rules to follow. No map of the environment is available a priori. The environment is perceived through a planar light detection and ranging sensor. The mission of the AGV is to move from its initial position to a given target position safely and as fast as possible. In this dissertation, a model predictive control (MPC)-based obstacle avoidance algorithm is developed to achieve the objectives through an iterative simultaneous optimization of the path and the corresponding control commands. MPC is chosen because it offers a rigorous and systematic approach for taking vehicle dynamics and safety constraints into account. Firstly, this thesis investigates the level of model fidelity needed for an MPC-based obstacle avoidance algorithm to be able to safely and quickly avoid obstacles even when the vehicle is close to its dynamic limits. Five different representations of vehicle dynamics models are considered. It is concluded that the two Degrees-of-Freedom (DoF) representation that accounts for tire nonlinearities and longitudinal load transfer is necessary for the MPC-based obstacle avoidance algorithm to operate the vehicle at its limits within an environment that includes large obstacles. Secondly, existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a novel nonlinear MPC formulation is developed. First, a new cost function formulation is used that aims to find the shortest path to the target position. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms of obstacle-free regions from an unstructured environment. Third, the no-wheel-lift-off condition is established offline using a fourteen DoF vehicle dynamics model and is included in the MPC formulation. The formulation can simultaneous optimize both steering angle and reference longitudinal speed commands. Simulation results show that the proposed algorithm is capable of safely exploiting the dynamic limits of the vehicle while navigating the vehicle through sensed obstacles of different size and number. Thirdly, in the algorithm, a model of the vehicle is used explicitly to predict and optimize future actions, but in practice, the model parameter values are not exactly known. It is demonstrated that using nominal parameter values in the algorithm leads to safety issues in about one fourth of the evaluated scenarios with the considered parametric uncertainty distributions. To improve the robustness of the algorithm, a novel double-worst-case formulation is developed. Results from simulations with stratified random scenarios and worst-case scenarios show that the double-worst-case formulation considering both the most likely and less likely worst-case scenarios renders the algorithm robust to all uncertainty realizations tested. The trade-off between the robustness and the task completion performance of the algorithm is also quantified. Finally, in addition to simulation-based validation, preliminary experimental validation is also performed. These results demonstrate that the developed algorithm is promising in terms of its capability of avoiding obstacles. Limitations and potential improvements of the algorithm are discussed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135770/1/ljch_1.pd

Application of Nonlinear Model Predictive Control to Holonomic Mobile Robots without Terminal Constraints or Costs

The use of mobile robots greatly enhances the capability and versatility of industrial robots compared to their fixed counterpart. However, successfully deploying autonomous mobile robots is challenging and requires accurate mapping, localization, planning and control. Herein, we focus the application of nonlinear model predictive control to a holonomic mobile robot while ensuring closed loop asymptotic stability. This thesis presents three main contributions in this area. We begin with a study of the regulation control of a holonomic mobile robots with limits on acceleration under a Model Predictive Control (MPC) scheme without stabilizing terminal conditions or costs. Closed-loop asymptotic stability is ensured by suitably choosing the prediction horizon length. We first compute a set of admissible states for a holonomic mobile robot with limits on acceleration using the theory of barriers. Then, by deriving a growth (envelope) function for the MPC value function, we determine a stabilizing prediction horizon length. Theoretical results are confirmed through numerical simulations. Next the Model Predictive Path Following Control (MPFC) of holonomic mobile robots is considered. Here, the control objective is to follow a geometric path, where the time evolution of the path parameterization is not fixed a priori, but rather is left as an extra degree of freedom for the controller. Contrary to previous works, we show that the asymptotic stability can be ensured for the resulting closed-loop system under MPFC without terminal constraints or costs. The analysis is based on verifying the cost-controllability assumption by deriving an upper bound on the MPFC finite-horizon value function. This bound is used to determine a stabilizing prediction horizon. The analysis is preformed in the discrete-time setting and results are verified by numerical simulations. Finally, a dual-objective MPC algorithm for an open chain manipulator is presented, which, as a primary objective takes the end effector to a desired position and as a secondary goal minimizes the effort required from the actuators. To achieve this, a recursive Newton-Euler algorithm is used to calculate the system dynamics and to determine the actuator torques. The proposed method is based on a time varying cost function which, as time goes on, reduces weight on the secondary objective. This allows the controller to minimize torque at the start of the maneuver without affecting the ability of the system to reach the desired end effector position. By taking advantage of the inherent benefits of MPC such as the ability to naturally incorporate constraints and to manipulate the objective function, the algorithms proposed here offer control solutions applicable in a variety of mobile robotic applications

Optimization based energy-efficient control inmobile communication networks

In this work we consider how best to control mobility and transmission for the purpose of datatransfer and aggregation in a network of mobile autonomous agents. In particular we considernetworks containing unmanned aerial vehicles (UAVs). We first consider a single link betweena mobile transmitter-receiver pair, and show that the total amount of transmittable data isbounded. For certain special, but not overly restrictive cases, we can determine closed-formexpressions for this bound, as a function of relevant mobility and communication parameters.We then use nonlinear model predictive control (NMPC) to jointly optimize mobility and trans-mission schemes of all networked nodes for the purpose of minimizing the energy expenditureof the network. This yields a novel nonlinear optimal control problem for arbitrary networksof autonomous agents, which we solve with state-of-the-art nonlinear solvers. Numerical re-sults demonstrate increased network capacity and significant communication energy savingscompared to more na ̈ıve policies. All energy expenditure of an autonomous agent is due tocommunication, computation, or mobility and the actual computation of the NMPC solutionmay be a significant cost in both time and computational resources. Furthermore, frequentbroadcasting of control policies throughout the network can require significant transmit andreceive energies. Motivated by this, we develop an event-triggering scheme which accounts forthe accuracy of the optimal control solution, and provides guarantees of the minimum timebetween successive control updates. Solution accuracy should be accounted for in any triggeredNMPC scheme where the system may be run in open loop for extended times based on pos-sibly inaccurate state predictions. We use this analysis to trade-off the cost of updating ourtransmission and locomotion policies, with the frequency by which they must be updated. Thisgives a method to trade-off the computation, communication and mobility related energies ofthe mobile autonomous network.Open Acces

Variational and Time-Distributed Methods for Real-time Model Predictive Control

This dissertation concerns the theoretical, algorithmic, and practical aspects of solving optimal control problems (OCPs) in real-time. The topic is motivated by Model Predictive Control (MPC), a powerful control technique for constrained, nonlinear systems that computes control actions by solving a parameterized OCP at each sampling instant. To successfully implement MPC, these parameterized OCPs need to be solved in real-time. This is a significant challenge for systems with fast dynamics and/or limited onboard computing power and is often the largest barrier to the deployment of MPC controllers. The contributions of this dissertation are as follows. First, I present a system theoretic analysis of Time-distributed Optimization (TDO) in Model Predictive Control. When implemented using TDO, an MPC controller distributed optimization iterates over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closed-loop with the plant. The resulting coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. When applied to time distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme. Second, I present the Proximally Stabilized Fischer-Burmeister (FBstab) algorithm for convex quadratic programming. FBstab is a novel algorithm that synergistically combines the proximal point algorithm with a primal-dual semismooth Newton-type method. FBstab is numerically robust, easy to warmstart, handles degenerate primal-dual solutions, detects infeasibility/unboundedness and requires only that the Hessian matrix be positive semidefinite. The chapter outlines the algorithm, provides convergence and convergence rate proofs, and reports some numerical results from model predictive control benchmarks and from the Maros-Meszaros test set. Overall, FBstab shown to be is competitive with state of the art methods and to be especially promising for model predictive control and other parameterized problems. Finally, I present an experimental application of some of the approaches from the first two chapters: Emissions oriented supervisory model predictive control (SMPC) of a diesel engine. The control objective is to reduce engine-out cumulative NOx and total hydrocarbon (THC) emissions. This is accomplished using an MPC controller which minimizes deviation from optimal setpoints, subject to combustion quality constraints, by coordinating the fuel input and the EGR rate target provided to an inner-loop airpath controller. The SMPC controller is implemented using TDO and a variant of FBstab which allows us to achieve sub-millisecond controller execution times. We experimentally demonstrate 10-15% cumulative emissions reductions over the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) drivecycle.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155167/1/dliaomcp_1.pd

A real-time robust ecological-adaptive cruise control strategy for battery electric vehicles

This work addresses the ecological-adaptive cruise control problem for connected electric vehicles by a computationally efficient robust control strategy. The problem is formulated in the space-domain with a realistic description of the nonlinear electric powertrain model and motion dynamics to yield a convex optimal control problem (OCP). The OCP is solved by a novel robust model predictive control (RMPC) method handling various disturbances due to modelling mismatch and inaccurate leading vehicle information. The RMPC problem is solved by semi-definite programming relaxation and single linear matrix inequality (sLMI) techniques for further enhanced computational efficiency. The performance of the proposed real-time robust ecological-adaptive cruise control (REACC) method is evaluated using an experimentally collected driving cycle. Its robustness is verified by comparison with a nominal MPC which is shown to result in speed-limit constraint violations. The energy economy of the proposed method outperforms a state-of-the-art time-domain RMPC scheme, as a more precisely fitted convex powertrain model can be integrated into the space-domain scheme. The additional comparison with a traditional constant distance following strategy (CDFS) further verifies the effectiveness of the proposed REACC. Finally, it is verified that the REACC can be potentially implemented in real-time owing to the sLMI and resulting convex algorithm

Optimal Control of Electric Bus Lines

Bus lines are inherently unstable systems, where any delay tends to be further amplified by the accrued passenger loads encountered at stops downstream. This self-reinforcing mechanism, when combined with the multiple sources of disturbances of an urban environment, can lead to the problem of bus bunching. To mitigate this, various types of control strategies have been proposed and some are routinely employed by transit agencies around the globe to improve service regularity. They range from simple rule-based ad-hoc solutions, to elaborate real-time prediction-based bus velocity control. However, most of these strategies only focus on service-related objectives, and often disregard the potential energy savings that could be achieved through the control intervention. Velocity-based control, in particular, is very suitable for eco-driving strategies, which can increase the energy efficiency of the transit system by adjusting the planned velocity trajectories of the vehicles based on the road and traffic conditions.This thesis proposes a scalable resolution method for the bus line regularity and eco-driving optimal control problem for electric buses. It is shown how this problem can be recast as a smooth nonlinear program by making some specific modelling choices, thus circumventing the need for integer decision variables to capture bus stop locations and avoiding the infamous complexity of mixed-integer programs. Since this nonlinear program is weakly coupled, a distributed optimization procedure can be used to solve it, through a bi-level decomposition of the optimization problem. As a result, the bulk of the computations needed can be carried out in parallel, possibly aboard each individual bus. The latter option reduces the communication loads as well as the amount of computations that need to be performed centrally, which makes the proposed resolution method scalable in the number of buses. Using the concept of receding horizons to introduce closed-loop control, the optimized control trajectories obtained were applied in a stochastic simulation environment and compared with classical holding and velocity control baselines. We report a faster dissipation of bus bunching by the proposed method as well as energy efficiency improvements of up to 9.3% over the baselines

Virtual Structures Based Autonomous Formation Flying Control for Small Satellites

Many space organizations have a growing need to fly several small satellites close together in order to collect and correlate data from different satellite sensors. To do this requires teams of engineers monitoring the satellites orbits and planning maneuvers for the satellites every time the satellite leaves its desired trajectory or formation. This task of maintaining the satellites orbits quickly becomes an arduous and expensive feat for satellite operations centers. This research develops and analyzes algorithms that allow satellites to autonomously control their orbit and formation without human intervention. This goal is accomplished by developing and evaluating a decentralized, optimization-based control that can be used for autonomous formation flight of small satellites. To do this, virtual structures, model predictive control, and switching surfaces are used. An optimized guidance trajectory is also develop to reduce fuel usage of the system. The Hill-Clohessy-Wiltshire equations and the D\u27Amico relative orbital elements are used to describe the relative motion of the satellites. And a performance comparison of the L1, L2, and L∞ norms is completed as part of this work. The virtual structure, MPC based framework combined with the switching surfaces enables a scalable method that allows satellites to maneuver safely within their formation, while also minimizing fuel usage