Martin Gulan

Implications of Inverse Parametric Optimization in Model Predictive Control

Recently, inverse parametric linear/quadratic programming problem was shown to be solvable via convex liftings approach [13]. This technique turns out to be relevant in explicit model predictive control (MPC) design in terms of reducing the prediction horizon to at most two steps. In view of practical applications, typically leading to problems that are not directly invertible, we show how to adapt the inverse optimality to specific, possibly convexly non-liftable partitions. Case study results moreover indicate that such an extension leads to controllers of lower complexity without loss of optimality. Numerical data are also presented for illustration.

Convex Lifting: Theory and Control Applications

This paper presents the concept of convex lifting, which will be proven to enable significant implementation benefits for the class of piecewise affine controllers. Accordingly, two different algorithms to construct a convex lifting for a given polyhedral/polytopic partition will be presented. These two algorithms rely on either the vertex or the halfspace representation of the related polyhedra. Also, we introduce an algorithm to refine a polyhedral partition, which does not admit a convex lifting, into a convexly liftable one. Furthermore, two different schemes will be put forward to considerably reduce both the memory footprint and the online evaluation effort, which play a key role in implementation of piecewise affine controllers. Finally, these results will be illustrated via numerical examples and a complexity analysis.

Control systems in omni-directional robotic vehicle with mecanum wheels

Mobile robotic systems are mechatronic devices that are currently becoming more and more complex. To design such a system, a combination of expertise from the fields of mechanical, electrical and computer engineering is required. This paper describes our custom omni-directional robotic platform designed for both indoor and outdoor use that contains a lot of prototypic hardware. All the designed components are interesting as they permit control of the robot as a complex mechatronic system. The main objective here was to use a larger amount of smaller control subsystems, rather than a central one. This is more advantageous from the control point of view. The electronics of the robot consists of microcontroller controlled distributed subsystems that are able to communicate with the master system. The following sections offer an insight into the control structures of the mobile robot.

Efficient Embedded Model Predictive Vibration Control via Convex Lifting

This paper presents an efficient real-time implementation of embedded model predictive control, adopted in the context of active vibration control with the objective of minimizing the tip deflection of lightly damped cantilever beams. In particular, we focus on memory and time-efficient explicit solutions of the associated constrained optimal control problems that are easily implementable on low-end embedded hardware. To this end, we exploit the concept of convex lifting and show how it can be used to devise low-complexity, regionless piecewise affine controllers without any loss of optimality and performance. The efficiency of this constructive procedure is quantified via an extensive complexity analysis, evidenced by a successful practical deployment and optimal vibration control performance using a family of 32-bit ARM Cortex-M-based microcontroller platforms.

Nonlinear Model Predictive Control with Moving Horizon Estimation of a Pendubot system

In this paper we present and investigate a complex control framework based on Nonlinear Model Predictive Control (NMPC) to achieve the unstable equilibria, and Moving Horizon Estimation (MHE) to estimate the actual state and parameters of a Pendubot. This fast, under-actuated nonlinear mechatronic system apparently poses a challenging benchmark problem that might benefit from a nonlinear optimization scheme. To overcome the related computational difficulties we make use of the ACADO Code Generation tool allowing to export a highly efficient Gauss-Newton real-time iteration algorithm tailored to the nonlinear model dynamics while respecting imposed constraints. We show simulation results illustrating the overall control performance of the closed-loop system as well as the advantages of the nonlinear MHE-based NMPC scheme.

Real-time implementation of an adaptive feedback and feedforward Generalized Predictive Controller

This paper is devoted to the measurable disturbance rejection problem in Generalized Predictive Control (GPC) using an adaptive GPC controller, which combines the process of online system identification and the process of generalized predictive feedback controller design. In this work, the GPC algorithm is extended to the case when the measurable disturbances are available for feedforward control. The proposed adaptive GPC algorithm with/without future disturbance compensation is implemented in real time and experimentally demonstrated for the application of motor revolutions tracking when subjected to deterministic and pseudo-random disturbance signals. The constraint handling capabilities of the controller are considered as well.

Construction of convex liftings based on halfspace representation

This paper presents a new algorithm to construct convex lifting for a given polyhedral partition whenever it exists. This algorithm exclusively relies on the halfspace representation of the regions in the respective partition. Also, this algorithm is applicable for the general polyhedral partitions of polyhedra, and thus overcomes the limitation on the polytopic partitions of the existing algorithm based on the vertex representation. Finally, the importance of the proposed algorithm is clarified via some numerical examples, in particular in implementation of piecewise affine controllers. Accordingly, the convex lifting concept is shown to be useful to both avoid storing the state-space partition and to facilitate the online evaluation.