Johan Åkesson

Modeling and Optimization with Optimica and JModelica.org—Languages and Tools for Solving Large-Scale Dynamic Optimization Problems

The Modelica language, targeted at modeling of complex physical systems, has gained increased attention during the last decade. Modelica is about to establish itself as a de facto standard in the modeling community with strong support both within academia and industry. While there are several tools, both commercial and free, supporting simulation of Modelica models few efforts have been made in the area of dynamic optimization of Modelica models. In this paper, an extension to the Modelica language, entitled Optimica, is reported. Optimica enables compact and intuitive formulations of optimization problems, static and dynamic, based on Modelica models. The paper also reports a novel Modelica-based open source project, JModelica.org, specifically targeted at dynamic optimization. JModelica.org supports the Optimica extension and offers an open platform based on established technologies, including Python, C, Java and XML. Examples are provided to demonstrate the capabilities of Optimica and JModelica.org.

CasADi -- A symbolic package for automatic differentiation and optimal control

We present CasADi, a free, open-source software tool for fast, yet efficient solution of nonlinear optimization problems in general and dynamic optimization problems in particular. To the developer of algorithms for numerical optimization and to the advanced user of such algorithms, it offers a level of abstraction which is notably lower, and hence more flexible, than that of algebraic modeling languages such as AMPL or GAMS, but higher than working with a conventional automatic differentiation (AD) tool.CasADi is best described as a minimalistic computer algebra system (CAS) implementing automatic differentiation in eight different flavors. Similar to algebraic modeling languages, it includes high-level interfaces to state-of-the-art numerical codes for nonlinear programming, quadratic programming and integration of differential-algebraic equations. CasADi is implemented in self-contained C++ code and contains full-featured front-ends to Python and Octave for rapid prototyping. In this paper, we present the AD framework of CasADi and benchmark the tool against AMPL for a set of nonlinear programming problems from the CUTEr test suite.

Feedback scheduling of model predictive controllers

The paper presents some preliminary results on dynamic scheduling of model predictive controllers (MPCs). In an MPC, the control signal is obtained by on-line optimization of a cost function, and the MPC task may experience very large variations in execution time from sample to sample. Unique to this application, the cost function offers an explicit, on-line quality-of-service measure for the task. Based on this insight, a feedback scheduling strategy for multiple MPCs is proposed, where the scheduler allocates CPU time to the tasks according to the current values of the cost functions. Since the MPC algorithm is iterative, the feedback scheduler may also abort a task prematurely to avoid excessive input-output latency. A case study is presented, where the new approach is compared to conventional fixed-priority and earliest-deadline-first scheduling. General problems related to the real-time implementation of MPCs are also discussed.

On dynamic real-time scheduling of model predictive controllers

The paper discusses dynamic real-time scheduling in the context of model predictive control (MPC). Dynamic scheduling in this setting is motivated by the highly varying execution times associated with MPC controllers. Premature termination of the optimization algorithm is exploited to trade off prolonged computations versus computational delay. A feedback scheduling strategy for multiple MPC controllers is also proposed, where the scheduler allocates CPU time to the tasks according to the current values of the cost functions. Simulated examples show how the overall control performance may benefit from the application of the proposed schemes.

Safe manual control of the Furuta pendulum

This paper deals with the manual control of unstable systems, subject to control signal saturation. In particular we consider the Furuta pendulum, where the problem is to control the orientation of the arm manually while stabilizing the inverted pendulum. This paper presents an analysis which leads to an insight into the problem as well as the control strategy. This control strategy has been implemented on the real Furuta pendulum. Aspects of the implementation as well as experimental results are discussed.

Object-Oriented Modeling and Optimal Control: A Case Study in Power Plant Start-Up

Modeling and optimization of complex systems traditionally have required significant programming efforts in order to encode the model dynamics, the cost functions and the constraints in a format suitable for state of the art numerical algorithms. The availability of dedicated languages for physical modeling has made the design process simpler, but often tools have been limited to a particular optimization algorithm. In this paper, we present a case study where a combined cycle power plant model has been developed using first principles in the modeling language Modelica. Based on the model, an optimal control problem for the start-up of the power plant has been formulated in the Optimica extension and solved using the open source software JModelica.org. The results demonstrate how high-level modeling languages and tools can be used to bridge the gap between the engineering need for intuitive description formats and the interfaces of efficient numerical algorithms. (Less)

Toolbox for development and validation of grey-box building models for forecasting and control

As automatic sensing and information and communication technology get cheaper, building monitoring data becomes easier to obtain. The availability of data leads to new opportunities in the context of energy efficiency in buildings. This paper describes the development and validation of a data-driven grey-box modelling toolbox for buildings. The Python toolbox is based on a Modelica library with thermal building and Heating, Ventilation and Air-Conditioning models and the optimization framework in JModelica.org. The toolchain facilitates and automates the different steps in the system identification procedure, like data handling, model selection, parameter estimation and validation. To validate the methodology, different grey-box models are identified for a single-family dwelling with detailed monitoring data from two experiments. Validated models for forecasting and control can be identified. However, in one experiment the model performance is reduced, likely due to a poor information content in the identification data set.

Design and Control of YAIP — an Inverted Pendulum on Two Wheels Robot

In this paper we describe the design and control of an inverted pendulum type robot on two wheels. The objective of the design is to provide a flexible platform intended for teaching and research, which provides rich opportunities for application of signal processing, control design, distributed control systems and consideration of implementational issues. In addition, a design constraint has been to use low-cost components. Issues such as selection of hardware and sensors, signal processing, modeling and control are treated. Special attention is given to the problem of obtaining high accuracy velocity estimates using analog encoder signals.

Efficient parallel solution of large-scale nonlinear dynamic optimization problems

This paper presents a decomposition strategy applicable to DAE constrained optimization problems. A common solution method for such problems is to apply a direct transcription method and solve the resulting nonlinear program using an interior-point algorithm. For this approach, the time to solve the linearized KKT system at each iteration typically dominates the total solution time. In our proposed method, we exploit the structure of the KKT system resulting from a direct collocation scheme for approximating the DAE constraints in order to compute the necessary linear algebra operations on multiple processors. This approach is applied to find the optimal control profile of a combined cycle power plant with promising results on both distributed memory and shared memory computing architectures with speedups of over 50 times possible.

Dynamic optimization with CasADi

We demonstrate how CasADi, a recently developed, free, open-source, general purpose software tool for nonlinear optimization, can be used for dynamic optimization in a flexible, interactive and numerically efficient way. CasADi is best described as a minimalistic computer algebra system (CAS) implementing automatic differentiation (AD) in eight different flavors. Similar to algebraic modeling languages like AMPL or GAMS, it includes high-level interfaces to state-of-the-art numerical codes for nonlinear programming, quadratic programming and integration of differentialalgebraic equations. CasADi is implemented in self-contained C++ code and contains full-featured front-ends to Python and Octave for rapid prototyping. In this paper, we discuss CasADi from the perspective of the developer or advanced user of algorithms for dynamic optimization for the first time, leaving out details on the implementation of the tool. We demonstrate how the tool can be used to model highly complex dynamical systems directly or import existing models formulated in the algebraic modeling language AMPL or the physical modeling language Modelica. Given this symbolic representation of the process models, the resulting optimal control problem can be solved using a variety of methods, including transcription methods (collocation), methods with embedded integrators (multiple shooting) as well as indirect methods.