Optimality of nonlinear design techniques: A converse HJB approach

The issue of optimality in nonlinear controller design is confronted by using the converse HJB approach to classify dynamics under which certain design schemes are optimal. In particular, the techniques of Jacobian linearization, pseudo-Jacobian linearization, and feedback linearization are analyzed. Finally, the conditions for optimality are applied to the 2-D nonlinear oscillator, where simple, nontrivial examples are produced in which the various design techniques are optimal

Constrained Finite Receding Horizon Linear Quadratic Control

Issues of feasibility, stability and performance are considered for a finite horizon formulation of receding horizon control (RHC) for linear systems under mixed linear state and control constraints. It is shown that for a sufficiently long horizon, a receding horizon policy will remain feasible and result in stability, even when no end constraint is imposed. In addition, offline finite horizon calculations can be used to determine not only a stabilizing horizon length, but guaranteed performance bounds for the receding horizon policy. These calculations are demonstrated on two examples

Constrained nonlinear optimal control: a converse HJB approach

Extending the concept of solving the Hamilton-Jacobi-Bellman (HJB) optimization equation backwards [2], the so called converse constrained optimal control problem is introduced, and used to create various classes of nonlinear systems for which the optimal controller subject to constraints is known. In this way a systematic method for the testing, validation and comparison of different control techniques with the optimal is established. Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC-based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and analyzed. Properties of MPC-based constrained techniques are then evaluated and implementation issues are explored by applying both nonlinear MPC and MPC with feedback linearization

A receding horizon generalization of pointwise min-norm controllers

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved

Nonlinear Games: examples and counterexamples

Popular nonlinear control methodologies are compared using benchmark examples generated with a “converse Hamilton-Jacobi-Bellman” method (CoHJB). Starting with the cost and optimal value function V, CoHJB solves HJB PDEs “backwards” algebraically to produce nonlinear dynamics and optimal controllers and disturbances. Although useless for design, it is great for generating benchmark examples. It is easy to use, computationally tractable, and can generate essentially all possible nonlinear optimal control problems. The optimal control and disturbance are then known and can be used to study actual design methods, which must start with the cost and dynamics without knowledge of V. This paper gives a brief introduction to the CoHJB method and some of the ground rules for comparing various methods. Some very simple examples are given to illustrate the main ideas. Both Jacobian linearization and feedback linearization combined with linear optimal control are used as “strawmen” design methods

On receding horizon extensions and control Lyapunov functions

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a control Lyapunov function based receding horizon scheme, of which a special case provides an appropriate extension of a variation on Sontag's formula. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem

Water for all : Proceedings of the 7th international scientific and professional conference Water for all

The 7th International Scientific and Professional Conference Water for all is organized to honour the World Water Day by the Josip Juraj Strossmayer University of Osijek, European Hygienic Engineering & Design Group (EHEDG), Danube Parks, Croatian Food Agency, Croatian Water, Faculty of Food Technology Osijek, Faculty of Agriculture in Osijek, Faculty of Civil Engineering Osijek, Josip Juraj Strossmayer University of Osijek Department of Biology, Josip Juraj Strossmayer University of Osijek Department of Chemistry, Nature Park “Kopački rit”, Osijek- Baranja County, Public Health Institute of the Osijek- Baranja County and „Vodovod-Osijek“ -water supply company in Osijek. The topic of World Water Day 2017 was "Wastewater" emphasizing the importance and influence of wastewater treatments on global environment. The international scientific and professional conference Water for all is a gathering of scientists and experts in the field of water management, including chemists, biologists, civil and agriculture engineers, with a goal to remind people about the significance of fresh water and to promote an interdisciplinary approach and sustainability for fresh water resource management. The Conference has been held since 2011. About 300 scientists and engineers submitted 95 abstracts to the 7th International Scientific and Professional Conference Water for all, out of which 33 was presented orally and 62 as posters. 47 full papers were accepted by the Scientific Committee. 38 full papers became the part of the this Proceedings while 9 papers were accepted for publication in Croatian Journal of Food Science and Technology and Electronic Journal of the Faculty of Civil Engineering Osijek - e-GFOS