The paper discusses the sensor selection problem in estimating spatial fields. It is demonstrated that selecting a subset of sensors depends on modelling spatial processes. It is first proposed to exploit Gaussian process (GP) to model a univariate spatial field and multivariate GP (MGP) to jointly represent multivariate spatial phenomena. A Mat\'ern cross-covariance function is employed in the MGP model to guarantee its cross-covariance matrices to be positive semi-definite. We then consider two corresponding \textit{univariate} and \textit{multivariate sensor selection} problems in effectively monitoring multiple spatial random fields. The sensor selection approaches were implemented in the real-world experiments and their performances were compared. Difference of results obtained by the univariate and multivariate sensor selection techniques is insignificant; that is, either of the methods can be efficiently used in practice.

The paper discusses the sensor selection problem in estimating spatial fields. It is demonstrated that selecting a subset of sensors depends on modelling spatial processes. It is first proposed to exploit Gaussian process (GP) to model a univariate spatial field and multivariate GP (MGP) to jointly represent multivariate spatial phenomena. A Mat´ern cross covariance function is employed in the MGP model to guarantee its cross-covariance matrices to be positive semi-definite. We then consider two corresponding univariate and multivariate sensor selection problems in effectively monitoring multiple spatial random fields. The sensor selection approaches were implemented in the real-world experiments and their performances were compared. Difference of results obtained by the univariate and multivariate sensor selection techniques is insignificant; that is, either of the methods can be efficiently used in practice.

The deep operator network (DeepONet) architecture is a promising approach for learning functional operators, that can represent dynamical systems described by ordinary or partial differential equations. However, it has two major limitations, namely its failures to account for initial conditions and to guarantee the temporal causality – a fundamental property of dynamical systems. This paper proposes a novel causal deep operator network (Causal-DeepONet) architecture for incorporating both the initial condition and the temporal causality into data-driven learning of dynamical systems, overcoming the limitations of the original DeepONet approach. This is achieved by adding an independent root network for the initial condition and independent branch networks conditioned, or switched on/off, by time-shifted step functions or sigmoid functions for expressing the temporal causality. The proposed architecture was evaluated and compared with two baseline deep neural network methods and the original DeepONet method on learning the thermal dynamics of a room in a building using real data. It was shown to not only achieve the best overall prediction accuracy but also enhance substantially the accuracy consistency in multistep predictions, which is crucial for predictive contro

Density of microalgae is critical information for production of algae in a closed cultivation system since it can be used to optimally control their growth rate, biomass concentration and quality of the products. Given advancement in image processing techniques and thanks to low-cost camera sensors, image based methods are increasingly widely utilized to indirectly estimate the density. Advantages of the image based techniques include being less invasive and more nondestructive and biosecured. However, most of the existing techniques rely on averaging all pixels of a microalgae image, which may eliminate crucial information of their spatial correlation. Therefore, in this work we propose to exploit a convolutional neural network (CNN) to efficiently extract information from the microalgae images, which are then employed to regress the density. Interestingly, the proposed deep CNN regression model accepts the whole color image as its input while the density is calculated in the output. The proposed CNN regression architecture was validated in real-world experiments where the microalgal strain Chlorella vulgaris was cultured and their images were captured by our low-cost camera sensor system. The obtained results demonstrate that the averaged estimation accuracy of the proposed model is 0.55\% (+/- 0.68\%) while the R2 value between the density predictions and the ground truths is 0.9997, which is highly accurate and practical.

The paper proposes a new approach to efficiently control a three-dimensional overhead crane with six degrees of freedom (DoF). In addition to five usual output variables including three positions of the trolley, bridge and pulley and two swing angles of the hoisting cable, it is proposed to consider elasticity of the hoisting cable, which causes oscillation in the cable direction. That is, there exists $6^{th}$ under-actuated output in the crane system. To design an efficient controller for the six-DoF crane, it first employs the hierarchical sliding mode control approach, which not only guarantees stability but also minimizes sway and oscillation of the overhead crane when it transports a payload to desired location. Moreover, the unknown and uncertain parameters of the system caused by its actuator nonlinearity and external disturbances are adaptively estimated and inferred by utilizing the fuzzy inference rule mechanism, which results in efficient operations of the crane in real time. More importantly, stabilization of the crane controlled by the proposed algorithm is theoretically proved by the use of the Lyapunov function. The proposed control approach was implemented in the synthetic environment for the extensive evaluation, where the obtained results demonstrate its effectiveness.

Identification of static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) is crucial for the success of system identification tasks. Identification of static nonlinear elements though can pose several challenges. Two of the main challenges are: (1) mathematical models describing the elements being unknown and thus requiring black-box identification; and (2) collection of sufficiently informative measurements. With the aim of addressing the two challenges, we propose in this paper a method of predetermining informative measurement points offline (i.e., prior to conducting experiments or seeing any measured data), and using those measurements for online model calibration. Since we deal with an unknown model structure scenario, a high order polynomial model is assumed. Over fit and under fit avoidance are achieved via checking model convergence via an iterative means. Model dependent information maximization is done via a D-optimal design of experiments strategy. Due to experiments being designed offline and being designed prior to conducting measurements, this method eases off the computation burden at the point of conducting measurements. The need for in-the-loop information maximization while conducting measurements is avoided. We conclude by comparing the proposed D-optimal design method with a method of in-the-loop information maximization and point out the pros and cons. The method is demonstrated for the single-input-single-output (SISO) static nonlinear element case. The method can be extended to MISO systems as well.

The paper presents a novel approach by using multi- step predictions to address the adaptive sampling problem in a resources and obstacles constrained mobile robotic sensor network to efficiently monitor environmental spatial phenomena. It is first proposed to employ the Gaussian process (GP) to represent the spatial field, which can then be used to predict the field at unmeasured locations. The adaptive sampling problem aims to drive the mobile sensors to optimally navigate the environment where the sensors adaptively take measurements of the spatial phenomena at each sampling step. To this end, a conditional entropy based optimality criterion is proposed, which aims to minimize prediction uncertainty of the GP model. By predicting possible measurements the mobile sensors potentially take in a horizon of multiple sampling steps ahead and exploiting the chain rule of the conditional entropy, a multi-step predictions based adaptive sampling optimization problem is formulated. The objective of the optimization problem is to find the optimal sampling paths for the mobile sensors in multiple sampling steps ahead, which then provides their benefits in terms of better navigation, deployment and data collection with more informative sensor readings. However, the optimization problem is nonconvex, complex, constrained and mixed-integer. Therefore, it is proposed to employ the proximal alternating direction method of multipliers algorithm to efficiently solve the problem. More importantly, the solution obtained by the proposed approach is theoretically guaranteed to be converged to a stationary value. Effectiveness of the proposed algorithm was extensively validated by the real- world dataset, where the obtained results are highly promising.

The paper addresses the problem of efficiently planning routes for multiple ground vehicles used in goods delivery services. Given popularity of today's e-commerce, particularly under the COVID-19 pandemic conditions, goods delivery services have been booming than ever, dominated by small-scaled (electric) bikes and promised by autonomous vehicles. However, finding optimal routing paths for multiple delivery vehicles operating simultaneously in order to minimize transportation cost is a fundamental but challenging problem. In this paper, it is first proposed to exploit the mixed integer programming paradigm to model the delivery routing optimization problem (DROP) for multiple simultaneously-operating vehicles given their energy constraints. The routing optimization problem is then solved by the multi-chromosome genetic algorithm, where the number of delivery vehicles can be optimized. The proposed approach was evaluated in a real-world experiment in which goods were expected to be delivered from a depot to 26 suburb locations in Canberra, Australia. The obtained results demonstrate effectiveness of the proposed algorithm.

The paper addresses the multimodal sensor selection problem where selected collocated sensor nodes are employed to effectively monitor and efficiently predict multiple spatial random fields. It is first proposed to exploit multivariate Gaussian processes (MGP) to model multiple spatial phenomena jointly. By the use of the Matern cross-covariance function, cross covariance matrices in the MGP model are sufficiently positive semi-definite, concomitantly providing efficient prediction of all multivariate processes at unmeasured locations. The multimodal sensor selection problem is then formulated and solved by an approximate algorithm with an aim to select the most informative sensor nodes so that prediction uncertainties at all the fields are minimized. The proposed approach was validated in the real-life experiments with promising results.

The paper addresses the problem of effectively controlling a two-wheel robot given its inherent non-linearity and parameter uncertainties. In order to deal with the unknown and uncertain dynamics of the robot, it is proposed to employ the adaptive dynamic programming, a reinforcement learning based technique, to develop an optimal control law. It is interesting that the proposed algorithm does not require kinematic parameters while finding the optimal state controller is guaranteed. Moreover, convergence of the optimal control scheme is theoretically proved. The proposed approach was implemented in a synthetic two-wheel robot where the obtained results demonstrate its effectiveness.

The paper addresses the problem of efficiently controlling a class of single input multiple output (SIMO) underactuated robotic systems such as a two dimensional inverted pendulum cart or a two dimensional overhead crane. It is first proposed to employ the hierarchical sliding mode control approach to design a control law, which guarantees stability and anti-swing of the vehicle when it is driven on a predefined trajectory. More importantly, the unknown and uncertain parameters of the system caused by its actuator nonlinearity and external disturbances are adaptively estimated and inferred by the proposed fuzzy logic mechanism, which results in the efficient operation of the SIMO under-actuated system in real time. The proposed algorithm was then implemented in the synthetic environment, where the obtained results demonstrate its effectiveness.

Adaptive sampling in a resource-constrained mobile robotic sensor network for monitoring a spatial phenomenon is a fundamental but challenging problem. In applications where a Gaussian Process is employed to model a spatial field and then to predict the field at unobserved locations, the adaptive sampling problem can be formulated as minimizing the negative log determinant of a predicted covariance matrix, which is a non-convex and highly complex function. Consequently, this optimization problem is typically addressed in a grid-based discrete domain, although it is combinatorial NP-hard and only a near-optimal solution can be obtained. To overcome this challenge, we propose using a proximal alternating direction method of multipliers (Px-ADMM) technique to solve the adaptive sampling optimization problem in a continuous domain. Numerical simulations using a real-world dataset demonstrate that the proposed PxADMM- based method outperforms a commonly used grid-based greedy method in the final model accuracy.