2018 (vol. 28) - Number 1

*I. Duleba, I. Karcz-Duleba:*

A comparison of methods solving repeatable inverse kinematics for robot manipulators

*A. Niederliński:*

A new approach for modelling uncertainty in expert systems knowledge bases

*T.T. Tuan, L.D. Tufa, M.I.A. Mutalib, N.M. Ramli :*

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

*M. Kaleta:*

Network winner determination problem

*A. Kowalewski:*

Extremal problems for parabolic systems with time-varying lags

*T. Rybus, K. Seweryn, J.Z. S±siadek:*

Application of predictive control for manipulator mounted on a satellite

*T. Kaczorek:*

Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices

*G. Grassi, A. Ouannas, V-T. Pham:*

A general unified approach to chaos synchronization in~continuous-time systems (with or without equilibrium points) as well as in discrete-time systems

*D. Pazderski:*

A robust smooth controller for a unicycle-like robot

ACS Abstract:

**2018 (Volume 28)**

Number 1

A comparison of methods solving repeatable inverse kinematics for robot manipulators

I. Duleba, I. Karcz-Duleba(Wroclaw University of Science and Technology, Poland) |

In this paper two recent methods of solving a repeatable inverse kinematic task are compared. The methods differ substantially although both are rooted in optimization techniques. The first one is based on a paradigm of continuation methods while the second one takes advantage of consecutive approximations. The methods are compared based on a quality of provided results and other quantitative and qualitative factors. In order to get a~statistically valuable comparison, some data are collected from simulations performed on pendula robots with different paths to follow, initial configurations and a~degree of redundancy.

**keywords:** manipulator, inverse kinematics, repeatability, optimization, algorithms

A new approach for modelling uncertainty in expert systems knowledge bases

A. Niederliński(University of Economics in Katowice, Poland) |

The current paradigm of modelling uncertainty in expert systems knowledge bases using Certainty Factors (CF) has been critically evaluated. A way to circumvent the awkwardness, non-intuitiveness and constraints encountered while using CF has been proposed. It is based on introducing Data Marks for askable conditions and Data Marks for conclusions of relational models, followed by choosing the best suited way to propagate those Data Marks into Data Marks of rule conclusions. This is done in a way orthogonal to the inference using Aristotelian Logic. Using Data Marks instead of Certainty Factors removes thus the intellectual discomfort caused by rejecting the notion of truth, falsehood and the Aristotelian law of excluded middle, as is done when using the CF methodology. There is also no need for changing the inference system software (expert system shell): the Data Marks approach can be implemented by simply modifying the knowledge base that should accommodate them. The methodology of using Data Marks to model uncertainty in knowledge bases has been illustrated by an example of SWOT analysis of a small electronic company. A short summary of SWOT analysis has been presented. The basic data used for SWOT analysis of the company are discussed. The 'rmes_EE' SWOT knowledge base consisting of a rule base and model base have been presented and explained. The results of forward chaining for this knowledge base have been presented and critically evaluated.

**keywords:** expert systems, uncertainty, certainty factors, knowledge bases, data marks, SWOT, SWOT knowledge base

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

T.T. Tuan, L.D. Tufa, M.I.A. Mutalib, N.M. Ramli (Universiti Teknologi Petronas, Tronoh, Malaysia) |

In advanced control, a control target tracks the set points and tends to achieve optimal operation of a process. Model predictive control (MPC) is used to track the set points. When the set points correspond to an optimum economic trajectory that is sent from an economic layer, the process will be gradually reaching the optimal operation. This study proposes the integration of an economic layer and MPC layer to solve the problem of different time scale and unreachable set points. Both layers require dynamic models that are subject to objective functions. The prediction output of a model is not always asymptotically equal to the measured output of a process. Therefore, Kalman filter is proposed as a state feedback to the two-layer integration. The proposed controller only considers the linear empirical model and the inherent model is identified by system identification, which is assumed to be an ample representation of the process. A depropanizer process case study has been used for demonstration of the proposed technique. The result shows that the proposed controller tends to improve the profit of the process smoothly and continuously, until the process reaches an asymptotically maximum profit point.

**keywords:** integrate economic optimization and MPC, Matlab-Hysys Interface, Kalman filter, integrate RTO-MPC, depropanizer

Network winner determination problem

M. Kaleta(Warsaw University of Technology, Poland) |

Many real-world marketplaces involve some additional constraints to be addressed during the market clearing process. This is the case of various infrastructure sectors of the economy, where market commodities are associated with some elements of the infrastructure, e.g., elements of telecommunication, power transmission or transportation network. Transactions are allowed only if the infrastructure, modeled as a flow network, is able to serve them. Determination of the best offers is possible by solving the optimization problem, so called the Winner Determination Problem (WDP). We consider a new subclass of the WDP, i.e., the Network Winner Determination Problem (NWDP). We characterize different problems in the NWDP class and analyze their computational complexity. The sharp edge of tractability for NWDP-derived problems is generally designated by integer offers. However, we show that some specific settings of the problem can still be solved in polytime. We also present some exemplary applications of NWDP in telecommunication bandwidth market and electrical energy balancing market.

**keywords:** network auctions, network winner determination problem (NWDP), complexity of the NWDP, MILP models, multi-commodity flow optimization, graph models

Extremal problems for parabolic systems with time-varying lags

A. Kowalewski(AGH University of Science and Technology, Poland) |

Extremal problems for parabolic systems with time-varying lags are presented. An optimal boundary control problem for parabolic systems in which time-varying lags appear in the state equations and in the boundary conditions simultaneously is solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.

**keywords:** boundary control, parabolic systems, time-varying lags

Application of predictive control for manipulator mounted on a satellite

T. Rybus, K. Seweryn(Space Research Centre (CBK PAN), Poland) | J.Z. S±siadek(Carleton University, Ottawa, Ontario, Canada) |

Specific conditions of on-orbit environment are taken into account in the design of all devices intended to be used in space. Despite this fact malfunctions of satellites occur and sometimes lead to shortening of the satellite operational lifetime. It is considered to use unmanned servicing satellite, that could perform repairs of other satellites. Such satellites equipped with a manipulator, could be used to capture and remove from orbit large space debris. The critical part of planned missions is the capture manoeuvre. In this paper a concept of the control system for the manipulator mounted on the satellite is presented. This control system is composed of the trajectory planning module and model predictive controller (the latter is responsible for ensuring precise realization of the planned trajectory). Numerical simulations performed for the simplified planar case with a 2 DoF manipulator show that the results obtained with the predictive control are better than the results obtained with adaptive control method.

**keywords:** space robotics, predictive control, trajectory optimization, free-floating manipulator

Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices

T. Kaczorek(Bialystok University of Technology, Poland) |

The notions of monomial generalized Frobenius matrices is proposed and the reachability and observability of positive discrete-time linear systems with positive and negative integer powers of the state matrices is addressed. Necessary and sufficient conditions for the reachability of the positive systems are established.

**keywords:** discrete-time, linear, positive, system, monomial Frobenius generalized matrix, reachability, observability

A general unified approach to chaos synchronization in~continuous-time systems (with or without equilibrium points) as well as in discrete-time systems

G. Grassi(Universita del Salento, Lecce, Italy) | A. Ouannas(University of Tebessa, Algeria) | V-T. Pham(Hanoi University of Science and Technology, Viet Nam) |

By analyzing the issue of chaos synchronization, it can be noticed the lack of a general approach, which would enable any type of synchronization to be achieved. Similarly, there is the lack of a unified method for synchronizing both continuous-time and discrete-time systems via a scalar signal. This paper aims to bridge all these gaps by presenting a novel general unified framework to synchronize chaotic (hyperchaotic) systems via a scalar signal. By exploiting nonlinear observer design, the approach enables any type of synchronization defined to date to be achieved for both continuous-time and discrete-time systems. Referring to discrete-time systems, the method assures any type of dead beat synchronization (i.e., exact synchronization in finite time), thus providing additional value to the conceived framework. Finally, the topic of synchronizing special type of systems, such as those characterized by the absence of equilibrium points, is also discussed.

**keywords:** chaos synchronization and control, scalar synchronizing signal, continuous-time system (with or without equilibrium points), discrete-time systems, observer-based synchronization, dead beat control, synchronization in finite time

A robust smooth controller for a unicycle-like robot

D. Pazderski(Poznań University of Technology, Poland) |

In this paper, a stabilizer dedicated for a unicycle-like robot is considered. The proposed smooth control law ensures the global boundedness of position and orientation trajectories to a neighbourhood of the desired point with an arbitrarily selected radius and it is robust to bounded additive measurement noises. The controller consists of a smooth hybrid navigation algorithm and a smooth feedback based on the transverse function approach. The stability proof, simulation and experimental results illustrating properties of the algorithm are discussed.

**keywords:** transverse functions, nonholonomic system, control motion task, Lie group, navigation vector fields, smooth feedbacks

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