This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.
We propose a class of m-crane control systems, that generalizes two- and three-dimensional crane systems. We prove that each representant of the described class is feedback equivalent to the second order chained form with drift. In consequence, we prove that it is differentially flat. Then we investigate its control properties and derive a control law for tracking control problem.
This paper briefly describes direct power control methods for two- and threelevel AC/DC converters and their modified DPC 3H 2-? and the DPC 5H2-? algorithms. It also presents two new control methods DPC-3Am (direct power control 3 areas with modification) and the DPC-3L-3Am (direct power control 3 levels 3 areas with modification). The research results were used to compare the described methods. The comparison was based on an average value of switching frequency and current distortion coefficient. Experimental investigations into the methods have shown that the use of the modified DPC methods reduces the number of switchings by more than 70% compared with the standard DPC method.
The paper describes a nonlinear controller design technique applied to a servo drive in the presence of hard state constraints. The approach presented is based on nonlinear state-space transformation and adaptive backstepping. It allows us to impose hard constraints on the state variables directly and to achieve asymptotic tracking of any reference trajectory inside the constraints, despite unknown plant parameters. Two control schemes (with and without integral action) are derived, investigated and then compared. Several examples demonstrate the main features of the design procedure and prove that it may be applied in case of motion control problems in electric drive automation.
The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.
Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.
Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.
Swing-up control of a single pendulum from the pendant to the upright position is firstly surveyed. The control laws are comparatively studied based on swing-up time from a given initial state to the upright position. The State Dependent Riccati Equation is found effective for designing the swing-up control law under saturating control input. The control law is extended to a linear combination of sine function of the angle and the angular velocity, and a variable structure control with a sliding mode given by the linear combination. Making the swing-up time correspond to a colour, which is similar to the Fractal analysis, colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like figures.
In the present paper .nite-dimensional, stationary dynamical control systems described by semilinear ordinary di.erential state equations with multiple point delays in control are considered. In.nite-dimensional semilinear stationary dynamical control systems with single point delay in the control are also discussed. Using a generalized open mapping theorem, su.cient conditions for constrained local relative controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin are formulated and proved. Roughly speaking, it will be proved that under suitable assumptions constrained global relative controllability of a linear associated approximated dynamical system implies constrained local relative controllability near the origin of the original semilinear dynamical system. This is generalization to the constrained controllability case some previous results concerning controllability of linear dynamical systems with multiple point delays in the control and with unconstrained controls. Moreover, necessary and sufficient conditions for constrained global relative controllability of an associated linear dynamical system with multiple point delays in control are discussed. Simple numerical example, which illustrates theoretical considerations is also given. Finally, some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non- minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.
This paper presents a control concept for a single-axle mobile robot moving on the horizontal plane. A mathematical model of the nonholonomic mechanical system is derived using Hamel’s equations of motion. Subsequently, a concept for a tracking controller is described in detail. This controller keeps the mobile robot on a given reference trajectory while maintaining it in an upright position. The control objective is reached by a cascade control structure. By an appropriate input transformation, we are able to utilize an input-output linearization of a subsystem. For the remaining dynamics a linear set-point control law is presented. Finally, the performance of the implemented control law is illustrated by simulation results.