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A priori error analysis for state constrained boundary control problems : Part II: Full discretization
This is the second of two papers concerned with a state-constrained
optimal control problems with boundary control, where the state constraints
are only imposed in an interior subdomain. We apply the virtual control
concept introduced in [26] to regularize the problem. The arising regularized
optimal control problem is discretized by finite elements and linear and
continuous ansatz functions for the boundary control. In the first part of
the work, we investigate the errors induced by the regularization and the
discretization of the boundary control. The second part deals with the error
arising from discretization of the PDE. Since the state constraints only
appear in an inner subdomain, the obtained order of convergence exceeds the
known results in the field of a priori analysis for state-constrained
problems. The theoretical results are illustrated by numerical computations
A priori error analysis for state constrained boundary control problems. Part II: Full discretization
This is the second of two papers concerned with a state-constrained optimal control problems with boundary control, where the state constraints are only imposed in an interior subdomain. We apply the virtual control concept introduced in [26] to regularize the problem. The arising regularized optimal control problem is discretized by finite elements and linear and continuous ansatz functions for the boundary control. In the first part of the work, we investigate the errors induced by the regularization and the discretization of the boundary control. The second part deals with the error arising from discretization of the PDE. Since the state constraints only appear in an inner subdomain, the obtained order of convergence exceeds the known results in the field of a priori analysis for state-constrained problems. The theoretical results are illustrated by numerical computations
A priori error analysis for state constrained boundary control problems : Part I: Control discretization
This is the first of two papers concerned with a state-constrained
optimal control problems with boundary control, where the state constraints
are only imposed in an interior subdomain. We apply the virtual control
concept introduced in [20] to regularize the problem. The arising regularized
optimal control problem is discretized by finite elements and linear and
continuous ansatz functions for the boundary control. In the first part of
the work, we investigate the errors induced by the regularization and the
discretization of the boundary control. The second part deals with the error
arising from discretization of the PDE. Since the state constraints only
appear in an inner subdomain, the obtained order of convergence exceeds the
known results in the field of a priori analysis for state-constrained
problem
Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot
Many robotic applications, such as milling, gluing, or high precision
measurements, require the exact following of a pre-defined geometric path. In
this paper, we investigate the real-time feasible implementation of model
predictive path-following control for an industrial robot. We consider
constrained output path following with and without reference speed assignment.
We present results from an implementation of the proposed model predictive
path-following controller on a KUKA LWR IV robot.Comment: 8 pages, 3 figures; final revised versio
Nonlinear Model Predictive Control for Constrained Output Path Following
We consider the tracking of geometric paths in output spaces of nonlinear
systems subject to input and state constraints without pre-specified timing
requirements. Such problems are commonly referred to as constrained output
path-following problems. Specifically, we propose a predictive control approach
to constrained path-following problems with and without velocity assignments
and provide sufficient convergence conditions based on terminal regions and end
penalties. Furthermore, we analyze the geometric nature of constrained output
path-following problems and thereby provide insight into the computation of
suitable terminal control laws and terminal regions. We draw upon an example
from robotics to illustrate our findings.Comment: 12 pages, 4 figure
Predictive Second Order Sliding Control of Constrained Linear Systems with Application to Automotive Control Systems
This paper presents a new predictive second order sliding controller (PSSC)
formulation for setpoint tracking of constrained linear systems. The PSSC
scheme is developed by combining the concepts of model predictive control (MPC)
and second order discrete sliding mode control. In order to guarantee the
feasibility of the PSSC during setpoint changes, a virtual reference variable
is added to the PSSC cost function to calculate the closest admissible set
point. The states of the system are then driven asymptotically to this
admissible setpoint by the control action of the PSSC. The performance of the
proposed PSSC is evaluated for an advanced automotive engine case study, where
a high fidelity physics-based model of a reactivity controlled compression
ignition (RCCI) engine is utilized to serve as the virtual test-bed for the
simulations. Considering the hard physical constraints on the RCCI engine
states and control inputs, simultaneous tracking of engine load and optimal
combustion phasing is a challenging objective to achieve. The simulation
results of testing the proposed PSSC on the high fidelity RCCI model show that
the developed predictive controller is able to track desired engine load and
combustion phasing setpoints, with minimum steady state error, and no
overshoot. Moreover, the simulation results confirm the robust tracking
performance of the PSSC during transient operations, in the presence of engine
cyclic variability.Comment: 6 pages, 5 figures, 2018 American Control Conferance (ACC), June
27-29, 2018, Milwaukee, WI, USA. [Accepted in Jan. 2018
Some applications of quasi-velocities in optimal control
In this paper we study optimal control problems for nonholonomic systems
defined on Lie algebroids by using quasi-velocities. We consider both
kinematic, i.e. systems whose cost functional depends only on position and
velocities, and dynamic optimal control problems, i.e. systems whose cost
functional depends also on accelerations. The formulation of the problem
directly at the level of Lie algebroids turns out to be the correct framework
to explain in detail similar results appeared recently (Maruskin and Bloch,
2007). We also provide several examples to illustrate our construction.Comment: Revtex 4.1, 20 pages. To appear in Int. J. Geom. Meth. Modern Physic
Optimal Pricing to Manage Electric Vehicles in Coupled Power and Transportation Networks
We study the system-level effects of the introduction of large populations of
Electric Vehicles on the power and transportation networks. We assume that each
EV owner solves a decision problem to pick a cost-minimizing charge and travel
plan. This individual decision takes into account traffic congestion in the
transportation network, affecting travel times, as well as as congestion in the
power grid, resulting in spatial variations in electricity prices for battery
charging. We show that this decision problem is equivalent to finding the
shortest path on an "extended" transportation graph, with virtual arcs that
represent charging options. Using this extended graph, we study the collective
effects of a large number of EV owners individually solving this path planning
problem. We propose a scheme in which independent power and transportation
system operators can collaborate to manage each network towards a socially
optimum operating point while keeping the operational data of each system
private. We further study the optimal reserve capacity requirements for pricing
in the absence of such collaboration. We showcase numerically that a lack of
attention to interdependencies between the two infrastructures can have adverse
operational effects.Comment: Submitted to IEEE Transactions on Control of Network Systems on June
1st 201
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