Improving model predictive controller turnaround time using restricted Lagrangians

We present a new application of proper orthogonal decomposition (POD) to optimal control. By restricting the Lagrangian of an optimal control problem to a suitable affine subspace, we can achieve a reduction in computational cost leading to faster turnaround times with minimal degradation in controller performance. An explicit algorithm for nonlinear model predictive control (NMPC) reduction using POD is presented along with some initial error analysis. To the best of our knowledge, this is the first time such an approach has been presented. We applied this approach to the control of a vehicle during a double lane change maneuver using NMPC and achieved 2 times faster turnaround times with excellent controller performance. This reduction approach for the development of real-time optimal controls is very promising and introduces some new research directions.This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC), the Toyota Motor Corporation and MaplesoftTM.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142387/1/2017_IEEE.pd

Nonlinear Model Predictive Control Reduction Strategies for Real-time Optimal Control

This thesis presents a variety of strategies to accelerate the turnaround times (TATs) of nonlinear and hybrid model predictive controllers (MPCs). These strategies are unified by the themes of symbolic computing, nonlinear model reduction and automotive control. The first contribution of this thesis is a new MPC problem formulation, called symbolic single shooting (symSS), that leverages the power of symbolic computing to generate an optimization problem of minimal dimension. This formulation is counter to the recent trend of introducing and exploiting sparsity of the MPC optimization problem for tailored solvers to exploit. We make use of this formulation widely in this thesis. The second contribution of this thesis is a novel application of proper orthogonal decomposition (POD) to MPC. In this strategy we construct a dimensionally-reduced optimization problem by restricting the problem Lagrangian to a subspace. This subspace is found by running simulations offline from which we extract the important solution features. Using this restricted Lagrangian we are able to reduce the problem dimension dramatically, thus simplifying the linear solve. This leads to TAT accelerations of more than two times with minimal controller degradation. The third contribution of this thesis is an informed move blocking strategy. This strategy exploits the features extracted in the restricted Lagrangian subspace to derive a sequence of increasingly blocked move blocking strategies. These move blocking strategies can then be used to reduce the dimension of the optimization problem in a sparse manner, leading to even greater acceleration of the controller TAT . The fourth contribution of this thesis is a new quasi-Newton method for MPC. This method utilizes ideas similar to singular perturbation-based model reduction to truncate the expression for the problem Hessian at the symbolic level. For nonlinear systems with a modest Lipschitz constant, we can identify the timestep as a `small' parameter about which we can do a perturbative expansion of the Lagrangian and its derivatives. Truncating to first order in the timestep, we are able to find a good approximation of the Hessian leading to TAT acceleration. The fifth contribution of this thesis is controller integration strategy based on nested MPCs. Using the symSS formulation we can construct an explicit model of a controlled plant that includes the full model as well as the MPC's action. This form of the controlled plant model allows us to generate exact derivatives so that fast solvers can be used for real time application. We focus here on the problem of planning and motion control integration for autonomous vehicles but this strategy can be extended for other problems that require accurate models of a controlled plant. The sixth contribution of this thesis is a strategy to handle integer controls in MPC based on a few reasonable assumptions: our predictions over the horizon are almost perfect and the future is inevitable. These assumptions enforce a degree of continuity, in the integer controls, between solutions over different timesteps that allow us to mitigate chatter and enforce a hard upper bound on solution complexity. This strategy constrains the integer solution of one timestep to be related to that of the previous timestep. Our results show that this strategy provides acceptable control performance while achieving TATs that are orders of magnitude smaller than those for conventional MINLP-based methods, thereby opening the door to new real-time applications of hybrid MPC

Trajectory Planning and Subject-Specific Control of a Stroke Rehabilitation Robot using Deep Reinforcement Learning

There are approximately 13 million annual new stroke cases worldwide. Research has shown that robotics can provide practical and efficient solutions for expediting post-stroke patient recovery. Assistive robots provide automatic limb training, which saves a great deal of time and energy. In addition, they facilitate the use of data acquisition devices. The data is beneficial in terms of quantitative evaluation of the patient progress. This research focused on the trajectory planning and subject-specific control of an upper-extremity post-stroke rehabilitation robot. To find the optimal rehabilitation practice, the manipulation trajectory was designed by an optimization-based planner. A linear quadratic regulator (LQR) controller was then applied to stabilize the trajectory. The integrated planner-controller framework was tested in simulation. To validate the simulation results, hardware implementation was conducted, which provided good agreement with simulation. One of the challenges of rehabilitation robotics is the choice of the low-level controller. To find the best candidate for our specific setup, five controllers were evaluated in simulation for circular trajectory tracking. In particular, we compared the performance of LQR, sliding mode control (SMC), and nonlinear model predictive control (NMPC) to conventional proportional integral derivative (PID) and computed-torque PID controllers. The real-time assessment of the mentioned controllers was done by implementing them on the physical hardware for point stabilization and circular trajectory tracking scenarios. Our comparative study confirmed the need for advanced low-level controllers for better performance. Due to complex online optimization of the NMPC and the incorporated delay in the method of implementation, performance degradation was observed with NMPC compared to other advanced controllers. The evaluation showed that SMC and LQR were the two best candidates for the robot. To remove the need for extensive manual controller tuning, a deep reinforcement learning (DRL) tuner framework was designed in MATLAB to provide the optimal weights for the controllers; it permitted the online tuning of the weights, which enabled the subject-specific controller weight adjustment. This tuner was tested in simulation by adding a random noise to the input at each iteration, to simulate the subject. Compared to fixed manually tuned weights, the DRL-tuned controller presented lower position-error. In addition, an easy to implement high-level force controller algorithm was designed by incorporating the subject force data. The resulting hybrid position/force controller was tested with a healthy subject in the loop. The controller was able to provide assist as needed when the subject increased the position-error. Future research might consider model reduction methods for expediting the NMPC optimization, application of the DRL on other controllers and for optimization parameter adjustment, testing other high-level controllers like admittance control, and testing the final controllers with post-stroke patients

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity